What is the difference between UCLA and UC Los Angeles?

There is no difference. UCLA and UC Los Angeles refer to the same campus of the University of California system, and UCLA is simply the standard abbreviation for the University of California, Los Angeles. In official and everyday use, people almost always say UCLA rather than “UC Los Angeles,” and the campus itself brands itself as UCLA.

This is different from how some other UC campuses are commonly named. For example, people say UC Berkeley or UC San Diego, but for Los Angeles, “UCLA” is the normal form in admissions, athletics, academics, and campus communications. You would not usually hear students, counselors, or the university call it “UC Los Angeles” in conversation.

If you are talking about applications, research, or programs, using “UCLA” is the clearest and most natural choice. In a formal sentence, “University of California, Los Angeles” is also correct, especially the first time you mention it. After that, “UCLA” is the expected abbreviation and will not confuse anyone.