I get that the title is vague, but that's kind of the problem. Basically, I've learned a jazzy version of the song "Heart and Soul" on the piano (you know, the one everyone learns to play with someone else). For reference, here's the sheet music (keep in mind, the first 6 bars are just jazzy stuff, pretend it starts on bar 7.
Someone asked me "if someone was playing the 'normal' [that is, the C Am F G version] of the song, and you played the jazzy version, would they 'fit together'?" I tried to explain that no, because for example halfway through bar 7, I play an F7 chord, while the standard version would play an Am chord, and these two chords are at odds, but she says "Oh that just sounds jazzy, not wrong". She hasn't played piano for years and doesn't know terminology so I couldn't get her to say what she meant in musical terms, but basically, she says that "If two people play heart and soul [that is, the same melody], and play chords 'in the key of c', then their two songs will fit together." I couldn't get her to explain what she meant by "In the key of C" though, whenever I probe she just says "Well I don't know what the musical terms technically mean". Basically, can you confirm that just because two people play songs with the same melody, and chords which go with that melody, their two versions don't have to align? Or am I crazy here?