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I am finding very different answers from various sources online regarding this topic.
Some say that the minor key is based on the natural minor scale, but harmonic and melodic minor can be used too. Others say that keys are not based on scales at all, which confuses me, because I thought keys indicate a tonic and a scale.
Does anybody know the correct answer?
Is a minor key based on a minor scale or did I completely misunderstand what a key is?
Historically, minor tonality is largely based on the Dorian mode, but regardless of which scale you take as the basis of minor tonality, you will find that in most contexts, the sixth and seventh degrees of the scale are frequently subject to chromatic alteration. It is certainly reasonable to describe this as "harmonic and melodic minor can be used too." (Although, taking the historical view once more, it is the existence of this tendency to use alteration that led to the development of the concepts of "harmonic minor" and "melodic minor" scales, not the other way around.)
By the 18th century, people tended to think more of the natural minor scale than of the Dorian as the "unaltered" basis of minor tonality, but because of the flexibility of ^6 and ^7, this has little practical effect on music other than on the choice of key signature. (I am aware of tonal music using "Dorian" signatures as late as J. S. Bach, but since modern editions usually change these key signatures, it's possible as far as I know that there were others using them even later, and it's conversely possible that Bach was one of few conservative holdouts doing so in the early 18th century.)
Others say that keys are not based on scales at all, which confuses me, because I thought keys indicate a tonic and a scale.
Key is definitely not the same as scale, but the two are, as you note, closely linked. To say that keys are not based on scales at all overstates the distinction to the point of being incorrect. Many misconceptions arise from the idea that keys are based on scales, but the existence of this misconception does not falsify the idea. Keys are in fact based on scales.
The question asks for "the correct answer". I don't think that's a realistic goal, and in a sense, a part of the OP's problem is the very assumption that there must be one correct meaning for the word "key" that we could find in some kind of ISO standard catalog of definitions. I see challenges with the feasibility of finding such correctness. Just to try something different, as an experiment, I try to answer from a subjective point of view, because after all, music is culture, people doing things and talking about it. The doing and talking is as diverse and ever-changing as people themselves, and failing to see the diversity is an obstacle to understanding music.
I don't play J.S. Bach and don't study the history of Western classical music, so I never use the term key in a historical sense. I also don't require the use of a leading tone in a piece to say it's in a minor key, even though I've heard that there have been people who do require such things. I don't have a lot of use for melodic and harmonic minor scales - they just mean temporarily altering some scale degrees, relative to the basic default scale i.e. reference grid that's given by the key signature. I consider key signatures as just convenient helpers - because pieces tend to use "in-key" notes very often, and a key signature reduces the amount of accidentals needed to write down a piece or passage of music.
What's common and what's not - I grew up in a culture where temporary accindentals were used in pieces all the time. When I was a small child, my aunt showed me some of the basics of musical notation, and accidentals were introduced within the first five minutes. Now G is sharp, now it's not sharp anymore. So what if there's an accidental somewhere, it doesn't change my feeling of balance and where the home chord is. You can use a B7 chord in a tune that's in A minor. (Much later I heard this is called a secondary dominant ... ooh what pompous names they have for simple everyday things)
What "key" meant for me was very practical. Whether the tune's center chord is minor or major, and how high it is. Well you can tell if a tune is in minor or major anyway, so stating that was kind of redundant, but ok. (edit: for those tunes that are ambivalent about which side is more prominent, saying "minor" or "major" is useful, because it tells which side they mean) Key was chosen according to who is singing and how high or low they could sing. Or if there are transposing instruments like saxophone or trumpet, let's select the key i.e. pitch height so that they don't have to play too many sharps or flats, if they aren't very good players.
Then, decades pass and the internet comes around and I see music.stackexchange. People asking questions about simple concepts like scale and key, as if they've had no practical touch with music-making, and are trying to construct music from theoretical formulas they found from random places. Tell me all rules of music. What is the correct definition of such and such term, how come there is a note that's "outside the key"... Umm, try it out in your own music in practice?
Ok. Now feel free to downvote and say that this approach for answering is against rules. ;) Music and life are about rules that can be programmed and calculated, right...?
Any minor key will have m3 between tonic and ^3. That is the defining factor. Whatever else happens in the notes involved in that key won't influence that fact.
EDIT: when I quote ^3, I mean the third letter of the alphabet - e.g. C>E♭, D>F♮, F♯>A♮, etc. That doesn't preclude minor pents, et al.
If a piece is based on the C natural minor, C harmonic minor or C melodic minor scales we can say it's 'in C minor'. (Some would argue over C natural minor being a 'key' as it lacks a complete dominant function.)
If based on C Phrygian or (unlikely) C Locrian, although these are 'minor modes' with a minor 3rd between ^1 and ^3, we don't. In the same way, although C Ionian, C Lydian and C Mixolydian are all 'major modes' with a major 3rd between ^1 and ^3, we only call the first one 'C major'.
Reason? Historical.
To really understand keys, scales and chords, you need to keep an eye on the essence of music: SOUND. Specifically, the overtone series, which is the physical basis of harmony, which in turn supports melody. The first notes of the harmonic series always form a MAJOR CHORD.
The notes used in a-minor come from the harmonic series based on C. All the notes of both keys can be formed with just 3 chords: the I, IV and V in C. CEG FAC GBD = CDEFGABC, or ABCDEFGA
In the key of a-minor, the iv and v chords are both minor. However, the major sound is stronger and more stable, so we like to substitute the major forms:
D-F#-A E-G#-B
Raising the 6th and 7th notes in this way gives the "ascending melodic minor."
There's a rule in theory: raised notes step up. So if your melody is moving downward, you generally wouldn't used raised notes. Therefore the "descending melodic minor" which has the # notes removed.
In the melodic minors, you are modifying the chords (and the key) to allow for nicer movement in scalar melodies.
However, sometimes a strong V-chord harmonic strength is so important that you will instead alter the melody to fit the chord. You will then use the exotic-sounding "harmonic minor," which refuses to give up the leading note (G# in the case of a-minor) no matter what, even if it means adding a large jump in the melody.
