As I'm also too lazy to LIU or do any research, I'll guess that it does, indeed, refer to the use of animals as transportation. "To ride" implies that you are seated upon the animnal; "to drive," that you are behind it, urging it along. When you drive a horse and carr, you are doing the latter, notwithstanding the fact that you are following the horse through no effort of your own.

The same is true, by analogy, with car and mo'bike. And, indeed, in the vast majority of cars, you do sit behind the engine, whilst on the vast majority of Motorbikes, you sit over it.

(This doesn't thoroughly explain it, of course, if you take into consideration that the earliest motor cars were rear-engined! hmmmm)