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No, that's not all it can mean. You can speak of driving a herd of animals, for instance, and the concept in relation to controlling a vehicle was, of course, first used in relation to horse-drawn vehicles, for which it is still used. Its use for cycling is less widespread, but see here:
Some cycling advocates have adopted the term in to use it in helping to emancipate cycling. Advocates like that generally favour equal treatment of cycling and motor vehicle driving, so while they wouldn't be in favour of separate laws like 'causing XYZ by ABC cycling', they would probably be in favour of laws that combined both the offences of 'causing XYZ by ABC motor vehicle driving' and the offences of 'causing XYZ by ABC cycling'. The placeholders are obviously to cover all the possible variations of such charges. Whether this sort of strategy works is a huge debate.
Advocates like that are, for the most part, US-based, where in view of the less liberal legal tradition and the fact that not only individual states but also some towns can (and often do) make their own laws/ordinances, campaigning on the law is far more important than it is here.
I thought "driving" was the act of controlling a motor vehicle?