Difference in types of distortion? (technicly speaking)

Heres what i understand from wikipedia and stuff

Type I distortion: The subtle warmth(from minute pitch bend) you get from analogue tape equipment

Type II distortion: driving the signal so it clips and folds adding new harmonics

The big one im confused about is waveshaping distortion, what is this doing to the signal? it seems like it does more than clip and fold

Also, why do huge basses sound better when there are small amounts of distortion applied alot? (rather than Alot once) Like is there some sideband thing going on or something

Theres just so many distortions out there, you got amp, tube, saturation, triode, tape. Not to mention all the ones that come with a plugin like ohmnicide.

Can these all be seperated into type I and II?

Distortion has always been the most mysterious effect, yet at the same time the most important!