Possibly a dumb question, but the recent tire threads had me thinking: what the heck kind of tires do I have on my bike and what if I want a different kind? Do I need a clincher rim to run clinchers and similarly with tubulars? I never see wheels for sale with a tubular vs clincher description, but is there a difference?

Okay, so this question is NOT whether clinchers or tubulars are better. Here is my predicament: I have a decent set of wheels on my bike, Bonti Race X Lites. They're somewhere between very solid training wheels and not so great race wheels. They are clinchers.