I'm going back a LONG time since I ever played with bicycle lights - but way back then some were AC and some were DC, it really makes no difference as far as incandescent bulbs are concerned.
However, bulbs never used to blow very much (I never had one fail), so presumably (like small motorcycle alternators) they are essentially self-limiting, as part of their basic design.
Considering power output is directly proportional to speed, full brightness is achieved at a fairly steady pace (15-20mph?), yet doing 60mph down a hill doesn't blow the bulbs - the same applies to small motorbikes - once you reach a certain speed the lights don't get any brighter.
As to what things are called, cars still use 'condensers' which changed to capacitors everywhere else many decades ago, and likewise all bycycle generators tend to be called dynamos by the cycling fraternity.
Thinking back, the last time I had any dealing with bicycle lights was with a work mate (about 15 years ago), he made a headlight for his bike using a 6V halogen spotlight (as used in shop displays - and I obtained some correct sized aluminium extruded tubing that just fitted it), he powered it from a 6V SLA battery - we used a bridge rectifier to provide charging for the battery. Obviously it didn't provide enough power to feed the bulb (50W!!) - but by running with the dynamo connected during the day, he was able to keep the battery charged enough for his purposes.
It was the brightest bicyle light I've ever seen