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For a while I thought they were one and the same, now I'm confused. This Wiki Article on the subject asserts that the blue note isn't even a real note, i.e. a note that's not part of the standard scales. Please elucidate this for me.

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    I'm not sure about that Wikipedia article. For one thing I don't think the explanation of equal temperament matches my understanding of why it was developed. And there is good reason to believe the notes and scales used in early 20th delta blues are actually based on the Muslim call to prayer that was brought over by west African Muslim slaves. – Todd Wilcox Dec 22 '15 at 2:44
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    @ToddWilcox: I'm not sure about the article either. As for the Muslim call to prayer: I'm not sure about that one either. The Transatlantic slave trade was banned unequivocally by Thomas Jefferson during the first month of his Presidency, unless I"m much mistaken. You're saying Muslim slaves waited nearly a whole century before introducing their tonal heritage to their music ... that's a stretch, kind of. In my opinion, anyway. – Ricky Dec 22 '15 at 4:12
  • @ToddWilcox I was sure enough that the direct link to equal temperament in that way was bogus to take it out. – topo Reinstate Monica Dec 22 '15 at 9:12
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    @ToddWilcox: Here's a Wiki article on the call to prayer: en.wikipedia.org/wiki/Adhan It never spread to any parts of Africa, it would seem. Africans (both northern and sub-saharan) had their own deep-sitting traditions. If you listen closely to Gregorian chants, you'll find that they resemble the blues as well. – Ricky Dec 22 '15 at 10:25
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    @ToddWilcox: The point I was making earlier is that all religious singing (or chanting) contains some form of blue notes and all other kinds of weird notes. Not to mention that singing a capella is conducive to using such notes. – Ricky Dec 22 '15 at 11:03
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There's no standard precise definition of what a blue note is. In some cases, a blue note could be seen as a deviation from the pitch of the note of a 'standard' (e.g. major) scale, but in other cases, blue notes are used in music whose tonality is far enough removed from the major or minor scale that those scales are arguably not sensible reference points to measure deviations from.

The quote in the Wikipedia article seems quite good:

Like the blues in general, the blue notes can mean many things. One quality that they all have in common, however, is that they are lower than one would expect, classically speaking. But this flatness may take several forms. On the one hand, it may be a microtonal affair of a quarter-tone or so. Here one may speak of neutral intervals, neither major nor minor. On the other hand, the lowering may be by a full semitone--as it must be, of course, on keyboard instruments. It may involve a glide, either upward or downward. Again, this may be a microtonal, almost imperceptible affair, or it may be a slur between notes a semitone apart, so that there is actually not one blue note but two. A blue note may even be marked by a microtonal shake of a kind common in Oriental music. The degrees of the mode treated in this way are, in order of frequency, the third, seventh, fifth, and sixth.

— Peter van der Merwe, Origins of the Popular Style, 1989

We can see from that explanation that blue notes are not simply the use of flattened notes that themselves still belong to the 12-tone scale, as blue notes can be quarter-tone deviations, or characterised as a glide though a frequency range.

Although the idea of blue notes is not restricted to the blues scale, this question - Exact pitch of blues scale notes - has some relevant answers. In particular, you can see from my answer there that I think that there's a note in the blues scale that is - in a guitar context, at least - played as a raised fourth more than a flattened fifth, though it may depend on the style in question (and of course such a distinction would be meaningless on the piano.)

When talking about 'blue intervals', we normally mean intervals from the root - so the 'blue third' is some kind of (altered) third above the root.

A tritone is simply an interval of three tones. So we can say that a note an interval of a tritone above the root could have the same frequency as a 'blue note' played between the fourth and fifth. That's not to say that a tritone above the root is a blue fifth though - blue notes are more complex than that.

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They are two different concepts completely, although the blue notes do typically take advantage of the tritone via harmony and melody.

A tritone is a specific interval of an augmented fourth (A4) or a diminished fifth (d5). It's a very special interval as it's the furthest distance in semitones you can be away from a note and it's dissonance and how it resolves is very central to a lot of compositions. A simple example from C to F♯/G♭ is a tritone. This interval is an essential part of the dominant 7th chord as the interval between the major third and the minor seventh in the chord is a tritone.

This leads us to the blue notes. Alone it's just notes to color the melody and harmony of a song, typically in a slightly dissonant fashion. The blue notes are ♭3, ♯4, ♭5, and ♭7 that are deviations from the typical major scale. From these notes tritones can be and are typically formed between other notes in the melody and harmony, but the notes themselves are not tritones. The ♯4 and ♭5 create a tritone with the tonic note. The ♭7 makes a tritone between itself and the 3 like in the dominant 7th chord. The ♭3 makes a tritone between itself and the 6 which is also root note of the relative minor of whatever major key you are in.

However, the blue note is not just used for there tritone properties, but also other properties as well including chromatic. It's pretty much standard to hear either 3, ♭3, 2 or 5, ♭5, 4 in a blues lick.

So in short the blue notes are notes added for flavor or color that can produce a tritone, but don't need to while a tritone is a well defined interval.

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    Okay, just to make sure I understand: the concept of the blue notes kind of includes ... uh ... contains, but isn't limited to, the tritone and its uses. And Wagner's constant pounding of the tritone in Tristan, which keeps the listeners in tonal suspense (denying them resolution till almost the very end of the piece) is not necessarily what jazz composers use the blue notes for. Correct? – Ricky Dec 22 '15 at 4:07
  • @Ricky the blue notes can be used to make tritones, but they alone are not tritones and have other applications such as chromaticism and tension. A tritone is an interval not a note. – Dom Dec 22 '15 at 4:14
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    I believe we're talking about the same thing. A blue note is also an interval. 3 is only an E if you're playing in C major; it becomes E-flat in C minor. – Ricky Dec 22 '15 at 4:19
  • @Ricky It's not an interval it's a note. In the context of other notes it can be, but the note alone is not an interval. – Dom Dec 22 '15 at 4:24
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    How? ... Are you saying you can just come up to a piano, press one key, step away, and claim (while keeping a straight face) that you've just played a blue note? – Ricky Dec 22 '15 at 4:29

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