So if you take a sine wave and put it through a non-linear transfer function, it experiences harmonic distortion, which produces other sine wave components at integer multiples of the original.
If you put 2 or more sine waves through the same non-linear transfer function, they experience intermodulation distortion, where the newly-produced partials are at sum and different frequencies from the originals.
But it seems strange that the 1-sine-wave case should be fundamentally different from the 2-or-more case.
As transfer functions with odd symmetry produce only odd-order harmonics, I thought maybe harmonic distortion is actually a form of intermodulation, where the single tone intermodulates with its negative frequency component, producing only odd harmonics (-10 and +10 are spaced 20 apart, producing intermodulation tones at 10+20 = 30, 10+20+20 = 50, 70, etc.) but that doesn't really work, because then why do even-symmetric transfer functions produce even-order harmonics and destroy the fundamental? And what happens when you distort a complex exponential that doesn't have a negative frequency component?