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?
http://www.thefreedictionary.com/motorcycle
http://www.thefreedictionary.com/motorbike
Best Answer
In my experience, mopeds are much more popular in Canada than the US. Having said that, (AmE here) I would say a moped was a rider-assisted lightweight motorbike intended for on-road use. A motorbike and dirt bike would differ by how they were conformed for their specific use: a dirt bike could be powerful but lightweight, have different suspension and tires than a motorbike (better known as a motorscooter) for street use. We often simply call these "bikes" when the context is already known (nice bike / that's a cute bike; I'd like one of those.)
Speaking as an average American (that is, I don't drive a motorcycle, but have three family members who do/did), a biker is reserved for a serious motorbike sports enthusiast, or a serious motorcyclist, with at least a very sweet (i.e. expensive/powerful) motorcycle that they ride either as a serious hobby (e.g. every weekend, and going to conventions, gatherings, etc.) or a true biker of old, think Easy Rider (or if that's way too far back for you, Sons of Anarchy.) (Then there are always the biker wannabes.) AFAIK, we don't have one specific designation for a lightweight bike user; he rides a motorcycle to work.... That's it from this little part of the world.