I know that it's usually stated that "aeolian is the same as our minor scale", but I think this can lead to misunderstanding. Yes, a 'natural' minor scale would start on the tonic and then rise tone, semitone, tone, tone, semitone, tone tone. However, when people play minor scales, they often play them as 'harmonic minor' scales, sharpening the seventh degree, or as 'melodic minor' scales, sharpening both the sixth and the seventh degree on the way up, then playing as you would in the aeolian mode on the way down. As a consequence, a lot of music written in a 'minor' key is not aeolian at all, but includes sharpened notes, particularly on the leading note (seventh degree).

My main point is simply that although the aeolian mode is the same as natural minor, what people imagine as minor, and what people have written in minor, is quite often not aeolian. So "aeolian = minor" is generally misleading.