As far as I know, "motorcycle" is the formal term -- and "bike" the informal one -- for a powered two (and occasionally three) wheeled vehicle resembling a bike but larger, heavier, and a heap more powerful, chiefly for one rider but sometimes having two saddles and a sidecar for passengers.
Besides, motorcycle riders are referred to fornally as "motorcyclists", and informally as "bikers".
Now, "motorbike" is the generic term for a lightweight, less powerful motorcycle with a smaller frame.
The thing is " motorbike" can both designate a lightweight motorbike (which I roughly equate with a dirt or pit bike stylewise), and also a pedal bicycle propelled by an attached motor (which, I guess, looks more or less like a moped).
Hence my question: how does what you Americans call a motorbike differ from a dirt (or pit) bike style vehicle, and from a moped?
Also, if "motorcyclist" and "biker" are both specific terms to refer to a motorcycle rider, what do you call someone that rides a motorbike? A motorbiker, or something else?