Can someone explain to me how these clutches work? It won't move but can't figure out which clutch to replace.

 

The one attached to the crankshaft is a centrifugal clutch, as used in some lawnmowers. Shoes, which have springs attached, fly round in the centre, as speed rises centrifugal force makes them grip the brake drum. These work fine as a rule until the brake linings wear to the steel backing so, if there is lining left on all shoes, the clutch will be OK. Other clutch is usually a normal motorcycle multiplate, yours is an unusual design, so I can't say if it is or isn't.