I have read that the physical vibration of coils(inductors) is the cause for noise but also that the inductor "overshoots" due to its stored energy.
Are these two distinct types of electrical noise?
Vibrating an inductor will cause it to vary in inductance in sync with the vibration. I remember one FM band oscillator with no microphone that allowed me to transmit my voice by shouting at it. "Honey, why are you shouting at the circuit?"
If you run current through an inductor, a magnetic field will build up around the inductor. When you disconnect the inductor from the current source, the magnetic field will collapse, giving the same kind of effect you expect when you move a bar magnet near an inductor. The voltage can get pretty high -high enough to fire the spark plugs in a car.