Yes. The verb "кататься" can mean different things depending on what you add to it. The core meaning is "to use a means of transportation (mostly for fun)".
Кататься на велосипеде to cycle
Кататься на лошади to ride a horse
Кататься на машине to drive/ride a car (for fun, mostly for the ride itself, not the destination)
Кататься на лыжах to ski + на чём угодно (whatever)
(mosfet07 meant that skating can also be translated into Russian in different ways, depending on f.ex. whether you meant skateboarding or in-line skating or something else.)
Yes, "кататься" is both to spend time riding/skating/driving/sailing/etc (for fun, as on a bicycle) and to roll (as on the floor).
I don't know if it is a coincidence, though. Ex: when I ride a bicycle (я катаюсь на велосипе́де), the wheels of the bicycle are literally rolling on the ground (катаются по земле).
Note that "кататься" is reflexive of "катать".