In the US, a university is a collection of colleges and graduate programs. It might have a general arts & sciences college (where one would major in things like literature, political science, psychology, chemistry, art history, etc.), some other specialize undergrad colleges/schools in programs like engineering, architecture, nursing, as well as graduate masters and PhD programs, law school, medical school, business school, and such. Smaller institutions that don't offer all the specialized schools and/or professional schools may call themselves colleges but issue bachelors degrees and perhaps Masters and PhD is arts & sciences type subjects.

Going to college in the US means a 4-year bachelors degree program, typically from roughly 18-22 years old. High school is the highest level of universal education, grades 9-12 (ages 14-18).