Real metal amps distort by increasing the size of the natural sine wave the guitar puts out beyond the size of the tube the signal is running through. This results in a square wave, because the smooth archs are cut flat by the physical tube. The tube is said to also compress the signal because the loudest sounds and quietest sounds become largely equal because the the signal is so large inside the tube that all notes come out at the same volume. The loudest just get chopped that much more.