I agree that all techniques are available all the time, and switching/blending becomes second nature over time. I guess we all develop our approaches differently and use different methods for different things. If I need a muted sound, as opposed to the muting of unplayed strings which is what the OP was asking about, I tend to favour my left hand. I damp with unused fingers, if there are frets I play on the fret such that the fingertip acts as a mute, on fretless I might stop the string just shy of the fingerboard in the same way as a string-bass player can play beyond the fingerboard, or I might use any combination thereof.