There is one possible difference. "You are right." can imply a moral position (sometimes but not always). "You are correct." usually implies a correct "fact."

They mean the same thing. "Correct" sounds a little more formal/proper to me and "right" more casual. But really I probably use both phrases 50/50 without any distinction.

Native speakers use "right" if we are discussing, possibly arguing (conflict) in order to diffuse tension and show support to the person speaking. In this way, it does not necessarily mean we agree with their perspective.

If someone was answering a question in a formal setting such as a classroom, I would use the word, "correct." If someone was answering a friendly, casual question, I would use the word "right." If it was a quiz show, I'd use either.