Anything added is distortion. Piano, for instance, has overtones stretched over harmonics.
… best we agree to disagree on that one. Technically you are correct of course, however in music reproduction I prefer an amp that adds 5% 2nd order harmonics over one which adds 0.01% 5th order harmonics. The vast majority of posters here will make the same choice in a listening test.
I’m looking at distortion in the context of how we experience music vs. what a scope will show.