English term (edited): crushing distorsion

Various types of distortion are possible, but 'crushing' sounds to me like one particular type, apparently popular where the sound appears to be 'crushed'.
Although I am no expert in guitar matters, my good friend who is always refers admiringly to this as 'saturation' — while I, as a hi-fi purist, am wincing at what to me is a serious audio defect! Technically, of course, it is indeed 'saturation' — where at some stage in the amplification process, the electronics are 'saturated' so that the output signal no longer corresponds to the input signal.