I FINALLY FIGURED IT OUT!

It wasn't in a different FF game at all. At least, not exactly.

YouTube - Final Fantasy VIII Review (Part 7)

The review starts off with the Celtic Moon version of the theme. I remembered this and couldn't quite place it so I just figured this other version of the Mysidia Theme must be part of a later game. I had no idea about the cover album until earlier today.

I am really glad I figured it out.