Diode types will have a general range, but there's always going to be some degree of variance.
The diode's Vf will determine how quickly the signal starts to clip. Lower Vf = clipper starts sooner/less output into the next stage.
In the context of fuzz/distortion/OD, I'm not super convinced that any particular diode has "a sound" but some people may disagree. To my ears a Si BAT46 sounds exactly the same as a germanium with a similar Vf.