They have the same literal meaning, but "correct" is generally a pretty hard assertion of, well, correctness - If you say something, and someone else says "corr

They have the same literal meaning, but "correct" is generally a pretty hard assertion of, well, correctness - If you say something, and someone else says "correct" in response, it can come across as demeaning, as if they are passing judgement on what you've said and found it sufficient (as elaborated on in the grandparent - the feeling is "what right do you have to decide the correctness of my comment?"). What if they were wrong, would you have said "incorrect"? In comparison, saying something like "right", "yes", are acknowledgements that don't carry the same weight when it comes to judging the actual content of what someone has said. Writing it out makes it sound like a strange response, but these things aren't always sensible. I would suspect it has roots in the typical contexts where you'll see "correct" being used - eg. tests and the like, where someone with authority (eg teacher/professor) is typically deciding on whether you're correct, as opposed to say, work, where generally these will be conversations between equals.