Come to think of it, is that jingle even used in the final S&K? It's sound #32 in the Sound Test, for anyone who doesn't know what I'm talking about.
If I recall correctly, that jingle in the final is at the end of the credits music, Sky Sanctuary fades into it. I don't think it was ever used standing alone, and the ending does indeed end slightly differently, much more abrupt.
Going completely from memory there since it's 6am, not slept. Might be wrong, 99.9% sure I'm not.