Well, you are confusing scales and keys, two different things - as is that wikipedia quote - but the point that the key of C major's "relative minor" key, in classical lingo, A minor, with the same key signature, uses the Aeolian, since A to A using the C major notes is Aeolian, is a good one, thanks.
[looks at the page] Wow, the scale of "A minor" has a wikipedia page?!..uh no, it seems it's about the key of A minor, and the whole thing confuses the key and the associated scale. That's very weird!
To explain slightly - in my understanding, saying a classical piece is "In C minor" as they do, usually means it starts and ends (at least) in the key of C minor. "C" means the root or I of the home/tonic chord is C, "minor" means the third is Eb ("major" would mean it's E). The fifth is always G, so not specified. This key specifies the (most important/initial) root triad. It says nothing about the other notes of the scale. The most important chord besides the I chord, the V7, has a B natural, which will usually occur often in the melody, and is not in the "natural minor" scale. Etc. Key =/= scale.
There are differences between scale and key, yes, but they often are interchangeable and overlap. For instance that wikipedia page for A minor doesn't say "A minor scale" nor "A minor key"... you can see they treat it (there and elsewhere) as if they are essentially the same thing in most usages. When necessary they make the distinction.
Another example from Wikipedia, from the "key" page: "In music theory, the key of a piece is the group of pitches, or scale, that forms the basis of a music composition in classical, Western art, and Western pop music."
I don't think Wikipedia is alone in this.
I'll admit I sometimes use the words "scale" (as well as the word "note") when I might have used "key" because it can get ambiguous and confusing given the overlapping meanings (such as a "piano key").
[looks at the page] Wow, the scale of "A minor" has a wikipedia page?!..uh no, it seems it's about the key of A minor, and the whole thing confuses the key and the associated scale. That's very weird!
To explain slightly - in my understanding, saying a classical piece is "In C minor" as they do, usually means it starts and ends (at least) in the key of C minor. "C" means the root or I of the home/tonic chord is C, "minor" means the third is Eb ("major" would mean it's E). The fifth is always G, so not specified. This key specifies the (most important/initial) root triad. It says nothing about the other notes of the scale. The most important chord besides the I chord, the V7, has a B natural, which will usually occur often in the melody, and is not in the "natural minor" scale. Etc. Key =/= scale.