Well. there are some interesting answers here. IF, you overdrive the front-end of an amp, it is because you can (when one attempts to turn the volume up past the voltage allowed by the preamp circuitry operating voltages for clean operation within spec those devices, tubes or transistor (opamp) must begin to "clip", a state made possible by the designer of that amp). Look at a hi-end stereo amp and the ratio of those voltages are kept within component spec to produce a pristine, clean uncompressed sound. This is simple compression. Simple compression can be described as pushing a big signal into a smaller "pipe", the tops and bottoms get flattened out. Early guitar compression was also desirable for the natural distortion of that process. The little EH LPB-1 had close to 10-to-1 ratio of signal boost to shove down the throat of whatever amp we wanted to "fatten up"; that is a LOT of signal. The audible effect of compression depends on the amount, if we go medium there are two overall differences imposed on the original signal, the fatter signal feeds itself back, thus sustain, and "limiting", a degree to which tones sent out the speakers tend to be a similar level. So, it can depend a lot on what the individual artist wants, and there are compression devices that offer control of many parts of that effect. When I have run a compressor, many times it is because I will be playing in a power-trio and the limiting properties work for me by keeping the individual note playing, riff or leads, nearly the same as when playing chords, thus little or no drop-out in the overall sound. The sustain is always useful. All of that said, most distortion devices mimic compression taken over the top, but well controlled.