Well, from an electrical standpoint, distortion is distortion, It's all some form of clipping, but might mean a hard square wave. But it does mean clipping in some form. How much clipping and the eq particulars of each amp and pedal vary. for example, just the very tops of the wave can be clipped (more like overdrive, not very distorted), or it's pushed into full square wave, which just sounds awful and buzzy and not very useful IMO.
My explanation was about distortion in general, but it applies everywhere - amps, speakers, all of it. But this is why all the guys are saying that distortion is bad for speakers, eg, if you have an uber powerful amp that sends a HUGE clean signal to a speaker that can't reproduce it, then you get a square wave at the
speaker level, which kills it. But if you mash that signal long before it gets to the speakers - like with a pedal, or by overdriving the gain, as in the Rumble's overdrive circuit, it's controllable by the master volume. That way you have your cake and eat it too - wildly distorted sound, but at a lower volume that's controlled by the master so it's safe for the speakers to reproduce. However, that signal is still a clipped signal, and the louder it is, the harder it is for the speaker to reproduce it. But to be clear, the thing you don't want to do is to send to the speakers themselves in a square wave. the square wave is like 0db > +100% db > 0db > -100%db, etc etc, doing it many times per second. That makes the speaker go off-on-off-on-off-on... which they're try to do, but probably can't cool the vpoicecoil, and depending onthe powere they are receiving, over extend the cone, too. God, there are so many ways to fry a speaker... I've even seen them catch fire. They'll fart out before this, so you have warning. very small warning, though.
But even having said all that, if you run a super-bassy sound of the proper voltage and wattage into speakers with voice coils that can't cool themselves down over the long run of you playing it that way, the voice coils will burn up and the speaker dies (see fire reference above). You might not hear any farting under those circumstances. It all depends on the speaker.
I had a GK MB210 that made a burning plastic aroma every time I got near the volume at which I usually play. That was my sign that the speakers weren't for me. In other words, always keep your ears (and nose, in my case) open to trouble signs.
more info:
Distortion - Wikipedia, the free encyclopedia
Hope I answered that.