This is a general question about harmonics generation, and how best to understand, generate, utilize, control these kinds of overtones, for sound design and in the mix...

I understand the basic benefit of harmonics in increasing psycho-acoustic presence, loudness, richness, thickening, width, etc... and adding something almost like a "chorusing" effect to beef-up a range of sounds (bass subs, mids, leads, full mixes, and so on)...

I used to simply saturate/distort sounds to get my overtones, then EQ. For example, with bass/mid sounds in DnB. For more subtle work on drums or busses, I would just add gain, smash to taste then EQ. But now it seems there are a ton of plugins -- and many maybe competing theories -- on how to generate harmonics, and to use their benefits:

Stuff like Fielding DSP Reviver seem quite pure and subtle imho -- my analyser displays only one (measly?) overtone each for 2nd and 3rd harm respectively (John Tejeda big-ups this plug).... On the other hand, stuff like Voxengo Shinechilla /Vertigo VSM-3 go much further with many more "spikes" in the graph, more like into distortion territory (but also more control and flex)... Then there are general tape (2nd harmonic) vs tube sat (3rd harmonic) plugs, and then also more psycho-acoustic plugs like Sonnox Inflator...

So what's the difference between "pure harmonics" vs saturation/clipping, and why would you want to reach for one over the other? Any thoughts on this from more knowledgeable headz...?