The difference lies in the pickup! On those other instruments you will be using a contact mic (piezo-transducer) wheras the solid body guitar is using an inductive coil.
The contact mic is going to pickup only physical resonance whereas the the coil is measuring an electromagnetic field. Plucking the steel string induces a change in voltage in the coil. This means that the coil can pickup all sorts of interesting electromagnetic interference from the tube amplifier that is all frequency dependent and involve that in whatever feedback loops are occuring.