It's one of the more well-known differences in terminology between British and US English. Both are used to describe someone studying for their first degree at university after leaving school. 'I am a college student' or 'I am a student in college'. (US) 'I am a university student' or 'I am a student at university' (British) If a person says they are a college student in the UK it means something a bit different. It generally means you are studying something vocational (e,g mechanics, plumbing etc). We know what 'college' means in the American context too, but we don't use it like that. Likewise Americans will understand what university means, but they generally use the word 'college' instead.

I live in the southern U.S. In my experience institutions around here with the word college in the name offer two-year degrees (AA or AS) and if university is in the name they offer four-year and graduate degrees.