First of all, according to the level, the junior college is lower than the university, which is the name of the famous university you said. In nature, there are public, private and office-run ones (for example, universities provide teachers and companies provide financial support). As long as it is a regular college affiliated to a regular university, no matter what school-running mode, it is recognized by the state. But when you graduate, you can still tell the difference.

For example, if it is a subordinate branch of a university, then the diploma will generally be written in XXX University. But if it is run by the people or by the government, the diploma will say, XXX University, XXX College. And there may be some differences between the issuing units of diploma and degree certificate.