With a fracture you would normally know the exact point at which the fracture occurred because:
(a) that's either the point which struck the ground with force or the place where you 'felt it go' when you fell ; and
(b) it's possible to point to, and touch, a PRECISE source of sharp pain.
With a sprain the pain is usually less localised and likely to have resulted from (say) your hand being knocked back when you landed on it, rather than from a direct shock to a specific bone.
Even if it's a fractured wrist though, a young fit person shouldn't need it to be in plaster for much more than a fortnight. (Written from experience!)
Chris