The meanings of the words college and university overlap.
A college is generally understood to be an undergraduate institution -- one that awards bachelor's degrees.
An institution that awards graduate degrees such as a master's degree or a doctorate is known as a university.
However, a university also awards undergraduate degrees.So, broadly speaking, a university is a larger institution that has a graduate school and often some research facilities, and a college is a smaller institution that has undergraduate teaching as its focus.
Some schools use both terms: a student at Harvard College is an undergraduate member of the Harvard University community. Most universities do not make this distinction, so if you are an undergraduate at the University of Michigan or at Brigham Young University, you simply refer to the institution as a university.
Therefore, a university can also be a college but a college can't also be a university.
A community college is an institution that grants a two-year associate's degree.