I can't speak to the first distorted guitar sound, but classic overdrive/distortion is just pushing the voltage of vacuum tube amplifiers out of the region wher

I can't speak to the first distorted guitar sound, but classic overdrive/distortion is just pushing the voltage of vacuum tube amplifiers out of the region where they amplify linearly ("over driving" them) to where the soft clipping introduces 2nd and 3rd and... nth order harmonics (harmonic "distortion") into the signal. And that's why it's called distortion and overdrive.