Difference between health center and hospital?

The main difference is that university hospitals are part of a university-medical school system, while other hospitals are... not.

University hospitals are teaching hospitals associated with, and (usually) on the campus of, a university medical school. Teaching hospitals are staffed by both experienced, licensed physicians, and newer licensed physicians-in-training, called residents. Medical students and student nurses often provide some of the care and routine duties under the supervision of licensed doctors and nurses.

University hospitals also perform a lot of research and medical studies.

Regular hospitals, often called "community hospitals," may or may not be teaching hospitals, but usually have fewer residents. Community hospitals tend to be smaller and have less comprehensive services, although this is not always the case.