I can't seem to find a straight definition for both.
A "scale", technically defined, is a sequence of ascending or descending "unit pitches" that form a palette of notes that can be used to form a melody. Most scales in Western music conform to a particular "key"; that is, a sequence of notes that will be "sharp" or "flat" by default. Not all scales have keys; the chromatic scale is a scale of all possible semitone steps used in Western music, while the whole-tone scale is a scale composed of intervals two semitones apart.
Within a particular key, there are 7 notes in a single octave, before reaching the 8th note which is named the same as the first note and is at double the frequency. The seven notes have differing intervals between adjacent notes; sometimes it's one half-step (semitone), while other times it's a whole step (two semitones). The pattern of whole-step/half-step intervals that determine the notes of a key, starting from the note for while the key is named, is whole-whole-half-whole-whole-whole-half. Within a single key, each of those seven notes could be used as the "base" note of an ascending sequence. Each such sequence, created by starting on a different note in the key, is a "mode" of that key, and each mode has a name:
More reading: Wikipedia - Musical Mode
A scale is any sequence of ascending (or descending) notes that can be used as an "organizing structure" for a piece of music. There are many types of scales, including diatonic (the "standard" in Western music), chromatic (containing every half note in an octave), whole-tone (containing notes a whole step apart), and pentatonic (the pentatonic formed from C major uses the "black" keys on a piano). They can even include quarter-tones and other microtones in the music of other cultures, such as Middle Eastern or gamelan music.
A mode is a very specific type of scale, with origins lying in Ancient Greek music; the names for the modes come from these traditions. Although they may look at times like standard diatonic scales, their origins are very different. For instance, the Lydian mode, which "looks" like C major, is actually F, G, A, B, C, D, E, F rather than C, D, E, F, G, A, B, C. The difference means that C major is whole-whole-half-whole-whole-whole-half, while Lydian mode is whole-whole-whole-half-whole-whole-half. (If transposed to C major, the mode would be C, D, E, F#, G, A, B, C.)
A good example to listen to is Bruckner's Os justi meditabitur, which is written entirely in the Lydian mode—but essentially notated in C. It doesn't "sound" like it's in C, though; that's the result of its modal foundation instead of a standard diatonic scale.
While the terms can be used fairly interchangeably, that only speaks to the practical applications; where each comes from is slightly different.
A scale is an ordered sequence of notes with a start and end. A mode is a permutation upon a scale that is repeatable at the octave, such that the start and end points are shifted.
For example, the major scale is repeatable at the octave. Since it contains seven distinct pitch classes within the space of an octave, there are seven possible modes on the major scale. These are known as the church modes, and have different names like Ionian, Aeolian, Dorian, Lydian, etc.
Major pattern in half/whole steps:
2nd mode of major (Dorian) in half/whole steps:
Modes in general, however, are not limited to this. You can extend the definition to other octave-repeatable scales. For example, consider the harmonic minor scale. Its pitches don't line up with those in the major scale or any of its modes, but the scale is repeatable at the octave. You can play in modes of the harmonic minor scale.
Harmonic minor pattern in half/whole/aug (augmented 2nd) steps:
5th mode of harmonic minor in half/whole/aug steps
Obviously, when you take a mode of a scale, the result is still an ordered sequence of notes; so you can call a mode a scale. And, for all scales that are octave-repeatable, you could, if you like, refer to them as modes. But for the reasons stated above, they are -not- the same in how they are generated. It is possible to have a scale that is not octave-repeatable (that takes up more notes than can be fit into an octave), but all modes come from a particular named scale (including the 1st mode of each scale, which is isomorphic to the scale).
I think the musical answers already given are the most useful, but the dictionary answers may also be informative. From the Oxford English Dictionary (OED) we get:
Scale: Any of the graduated series of sounds into which the octave is divided, the sounds varying according to the system of graduation adopted.
Mode: A scheme or system specifying the disposition in a scale of the constituent notes of a melody or harmony; spec. each of a conventionally agreed set of such schemes or systems.
The OED also notes each word's first recorded use (with this meaning). For 'scale' it comes in T. Morley's 1597 'Plaine & Easie Introd. Musicke', where he writes "Here is the Scale of Musicke"; while for 'mode' it is C. Simpson's 1667 'Compend. Pract. Musick' where he writes "That which the Grecians called Mode or Mood". The next printed occurrence for 'mode' listed in the OED is A. Malcolm's 1721 'Teat. Musick" where he writes "I would propose the Word Mode, to express the melodious Constitution of the Octave"
Sorry, but I have to chime in after all this time. The answers given here, while accurate, convey none of the most critical distinctions, nor of how modes sound to the ear in a way different from scales. And how things sound is what music is all about. Otherwise you may as well describe the difference between, say, Leonardo Da Vinci and Claude Monet by talking about the types of pigments each used.
Simply put, the real difference between a mode and a scale is one of tonality. A scale, in Western practice, has a tonal center to which the ear gravitates. The seventh scale step pulls the ear toward the tonic, and chords based on those half-steps feel as if they must be resolved in that direction. The statement
For a better discussion of this topic than I may hope to render in a few paragraphs here, I encourage you to listen to Leonard Bernstein's master class on this very topic, rendered in four parts on YouTube. He covers the physics of modes (scale steps and all that) better than others have done here, but also illuminates the chemistry, which is after all what separates real, organic music from academic discourse.
A mode is a type of scale.
Consider a Diatonic scale. For each tone in the scale (1, 2, 3, 4, 5, 6, or 7), you get a different mode when you start on that note.
Think of C Major:
C D E F G A B.
Notice how there are 7 notes.
There are 7 modes in a scale, one for each note of the scale.
Modes are the scale, starting from a different note. In this instance, C Major is the parent scale and all the modes are derived from it.
So using the notes of C Major we get:
C Ionian (The same exact thing as C Major) D Dorian E Phyrgian F Lydian G Mixolydian A Aeolian (The same exact thing as A Minor) B Locrian
In theory, if I play D E F G A B C D and the key of the song is in C Major, then I'm playing in D Dorian. However, actually using modes is a bit more complicated. There's as much theory with them as any other aspect of music. This is just an overview of what they are. In fact, you can spell modes relating them to major scales, which gives you formulas that you can use to make modes on the fly.
Try to stay with me.
So if I have D Dorian in C Major, I can think of it as D Dorian in C Major. But what if I don't know what the key is, or I don't know what the mode is? This is where parallel majors come in handy.
Parallel majors are just the major scale of whatever mode/scale you're playing in. So if I'm in D Minor, D Major is the parallel major. G Lydian's parallel major is G Major.
So let's say I have a lot of notes:
F G A B C D E F
And I don't know the key of the song. I can compare this to the parallel major just to see how it's different, and this will tell me which mode it is because every mode has its own formula, which make it unique. The notes of F Major:
F G A Bb C D E F
So comparing the notes that we had before to F Major, we realize we have a #4 (Bb to B). Lydian is the mode that has a #4, so the first group of notes I had was F Lydian!
You can repeat this process for any mode. In fact, I recommend spelling each mode against its parallel major to understand how they're different yet the same. Here's each formula for the 7 diatonic modes of the major scale:
Ionian: 1 2 3 4 5 6 7 (This is just the major scale)
Dorian: 1 2 b3 4 5 b6 7 (So D Dorian differs from D Major because D Dorian has a flat 3 and 6 while D Major doesn't)
Phyrgian: 1 b2 3 4 5 b6 7
Lydian: 1 2 3 #4 5 6 7
Mixolydian: 1 2 3 4 5 6 b7
Aeolian: 1 2 b3 4 5 b6 b7 (This is just the natural minor scale)
Locrian: 1 b2 3 4 b5 b6 7
The seven inversions of the major scale are the modes. So every mode is a scale; but not every scale is a mode (eg. the harmonic minor scale is not a mode).
Aeismail's answer is confusing - using the black notes on the piano will give either F# maj.pent (Gb maj pent.) or D# min.pent (Eb min pent). However, all the basic modes (dorian, mixolydian etc., ) are still scales - groups of notes that work with each other- but the only modes that are scales as we know them are the Ionian as in major, and the Aeolian as in the natural minor. It's interesting that a composer may state 'this is in D dorian, then writes in the key of Cmaj !! Also don't be messed up with the other naming method - the dorian OF C is in fact, D dorian !!
Assuming everyone is oriented to what music is for most practical purposes of the "western" world (which is code for European and Caucasian), scales are groups of notes whose absence of some of the notes which leaves spaces called intervals gives the scale its identity (regardless of octave where each repeats or key).
Modes are said to be scales too, but they are not if your definition of a scale is that all its notes are always sounded and the intervals between notes that are kept quiet. Modes then are the accounting for specific the possibilities of notes moved into those intervals which are now played (although not usually linearly)--each or which gives the scale it own NEW modal identity. Since there really aren't that many notes on a "western" instrument where the system of tones and semitones is only practical to be voice within a few perceptible octaves, modes are an identification system of sound for every scale where there is an interval to be shortened or lengthened. Modes unharness music to allow for new realms of character and individual style and signature of a composure or improvisationalist including dissonance. But unlike scales, it is almost never so that one plays a mode in its entirety completely linearly. I can sound like a mistake if not used deliberately to take the music in a new direction.
I miss the fundamental distinction between scale and mode in the answers here. A scale is an ordered set of notes (usually functionally repeating after an octave). A mode is the harmonic framework built from it. The difference is similar to that of floor tiles and a floor. Even if the floor contains nothing but floor tiles, it is conceptually different from the constituting tiles.
A mode is basically what you get from making musical and harmonic sense of a scale, putting the notes into relation with each other focused on the respective tonic, and using the various notes of the scale to build a harmonic framework.
A "mode" is simply a scale that has been altered in some way. The unaltered natural major scale is playing in Ionian mode. The unaltered natural minor scale is playing in Aeolian mode. The other modes can be constructed by altering the natural minor or major scales.
For example the Phrygian mode can be formed by a natural minor scale with a flattened 2nd.
A good explanation of this is given here: http://www.mandolincafe.com/niles2.html
All modes are scales but not all scales are modes. All scales try to achieve is to give you a series of notes that are a set pattern of whole tones and semi tones apart.
Take the Major scale for instance. This scales has two semi tones that are between 3/4 and 7/8 scale degrees. It does not matter on which note you start from if your semitones are at that place you have yourself a Major scale.
A mode is just a scale with the semitones in an unusual place. Dorian for instance has its semitones in between 2/3 and 6/7. It has the unresolved feeling to it because the leading tone is a whole tone from the tonic (Which is the antithesis of virtually all western music traditions). The same is true of Modes you can in this case start on any note and as long as your semi tones are where I mentioned you will have a Dorian.
They need to be consider in the same way you would consider any other scale.
A scale is an ordered set of notes, usually defined by a starting note and a pattern of intervals. For example, the C major ascending scale starts at the note “C” and follows the “major scale” pattern: tone–tone–semitone–tone–tone–tone–semitone. The starting note is called the tonic, first degree, or key of the scale, depending on context.
Notice that this is essentially the same pattern, but the first mode starts with the tone, and the second mode starts with the semitone. If you change the first degree and the mode in parallel, you get two scales with the same notes but a different starting point. For example:
You can apply the same principle to the major scale, which has seven modes. All of these modes of the major scale use the same notes, but a different first degree:
Note that when you start at the sixth degree and sixth mode of the major scale, you get the relative minor key, which has the same key signature. Likewise, if you start at the third degree and third mode of a natural minor scale, you get the relative major key.
Any scale with a mixture of intervals in its pattern will have modes like this. Common modal scales have names, like the Lydian scale for the fourth mode of the major scale or the Phrygian dominant scale for the fifth mode of the harmonic minor scale.
A scale is a set of notes. For instance, the D Dorian scale contains the notes D, E, F, G, A, B, C, and D.
A mode is a scale or scales with musical functions attached to the notes. For example, the Dorian mode of Gregorian chant (sample here) has
For another example, the minor mode of classical music consists of natural, harmonic, and melodic forms with downward and upward tendencies attached to the 6ths and 7ths.
I think some confusion here could be alleviated with a historical perspective. Many of the explanations above talk about present-day relations between the pair of major/minor "scales" and some altered versions of the same notes, reordered, equivalent to "modes" (white notes on the piano = C major scale = A Aeolian mode, D Dorian, etc.). This is doubtless correct in contemporary jazz theory. But there have also been some descriptions of the modes as "arbitrary" or having no tonal center, and that is not quite right, historically speaking.
The "church" modes (of which there were eventually 12) did indeed have tonal centers, just like the major and minor scales, which were, at one time, two of those 12 modes. (As people have noted above, major and minor were once called the Ionian and Aeolian modes.) In fact, modality is where the very notion of the "dominant" and "tonic" comes from: every tone (the old word for mode) used in Western music had both a "tonic" or "final" note and a "dominant" note; in addition, some of the tones had different "ambitus," or range above and (sometimes) below the final, its tonal “center of gravity."
In the first European systems we have record of, there were basically eight tones/modes, named after the Greek tonoi (but wrongly, as it happens -- ask me about that later. :) There were four "authentic" modes: Dorian, Phrygian, Lydian, and Mixolydian, often just called Mode I, II, III, and IV. From our contemporary perspective, it is convenient to memorize the modes by considering them as reorderings of the white note "C major" scale, but that scale did not even exist at this time. There were also four "plagal" modes, designated with the prefix Hypo-, as in Hypodorian. (I'm going to leave them largely out of this answer, for space reasons.)
Theorists of the Middle Ages and Renaissance went wild trying to derive all the modes in use from descriptions in rediscovered Greek theoretical texts, figuring out which names went with which notes, etc., but they made a mess of it.
Clear from practical treatises is that musicians basically thought about building modes by overlapping standardized hexachords, six-note scales, whose tones were named according to mnemonic syllables one sang, syllables designed to remind the singers where the half and whole steps were in the melodies they were singing.
UT = C
RE = D
MI = E
FA = F
LA = A
(To find out where the syllables came from, Google "Utqueant laxis.") I bet you recognize some of these singing syllables from ones laid out for the von Trapp kids by Maria in The Sound of Music, by which time "do" had replaced "ut" (easier to sing), and a seventh syllable, "ti," had been added because seven-note major scales had become fundamental to music.
But back in Ye Olden Tymes, there were only the six notes, with a MI-FA half-step in the middle. To sing melodies with a wider range, you shifted from one transposition of the hexachord to another, which was called "mutation." Here's how a medieval singer would have understood how to sing a full eight note scale in the Dorian mode:
See how radically different this is from modern scalar thinking? The octave is not important. (The two "D"s are sung to two different syllables!) The Dorian mode was constructed in practice by conjoining two identical tetrachords, each imagined as the center four notes of a hexachord built symmetrically around a single half-step interval: (C)D*EF*G(A) + (G)A*BC*D(E). Thinking about Dorian worked this way because it fit with the way Dorian mode melodies usually went: they would twist around in the lower tetrachord for a while, then move into the upper one, and eventually back down again. The two centers of modal attraction were the bottom note of the lower tetrachord, D, called the "final"; and the bottom note of the upper, A, called the "tenor," the reciting tone, or, sometimes, "the dominant."
You can run the same exercise for the three other authentic church modes, then play around with the ambitus by adding the second tetrachord below the final. Much later, someone figured out that two tetrachords where the MI-FA interval was at the "top" of each tetrachord (UT-RE-MI-FA + UT-RE-MI-FA) could be a mode, too. (It would have been sung: UT-RE-MI-FA-SOL-RE-MI-FA.) It was named Ionian by late Medieval theorists, and eventually, became the basis of the major scale.
But that's another story.