Community colleges are purely for education. You're not gonna have clubs, sports, greek life, extracurricular activities, and all that jazz at your local community college. You attend strictly for advancing your education in that field or program you want to take. The degrees aren't as abundant and only go up to an associate's at least for mine.
Universities, on the other hand, do generally have all those things(will be some exceptions here and there) while having an associate's and bachelor's degrees available in a large variety of different subjects. Most have graduate programs available. The overall vibe of a university is going to feel a lot grander. The exceptions would be the universities are specific in a field of study. M.I.T. for example, the Massachusetts Institute of Technology. The majority of colleges though are general where you can major in more or less anything.
Community colleges are also far cheaper and in some situations free(for example, at my local community college, high school students could take courses over the summer for free).