Isn't it the same when there's a signal and when there's silence?
When there's silence that would only be noise. Distortion happens only when there's a signal.
Does the thd "modulates" the signal so it takes a different form for every recording we make?
Distortion shows up as additional frequencies that were not present in the original signal. There's THD and also IM, though IM is generally more damaging because the added frequencies are not necessarily related musically to the original.