Does anyone know what the difference between NCAA, intramural, and club sports in college is?

i am looking at colleges now (I'm a senior in hs) and for the past ten years I did gymnastics. I would like to compete in college, but div II and III are my only realistic options and there are only a few schools. I was wondering if someone could explain better what club and intramural sports are in college. I think intramural you compete its just a little more laid back then NCAA? this could be good for me but I'm unsure of what it is and everyone I seem to ask seems unsure as well. any answers would really be helpful!
Does anyone know what the difference between NCAA, intramural, and club sports in college is?
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