I think "See you around" is a little more dismissive than the others. When you say "see you" or "see you later", it's usually to someone that you do see regularly (a co-worker, perhaps)- someone that you definitely will see again.
When you say "see you around" it's usually to someone that you don't see often or an old acquaintance that you met by chance; someone that you really don't care if you see them again or not.
See you (informal)
=>We will see each other again, maybe later, maybe tomorrow, maybe next week
See you around (informal)
=> I don't know when I will see you again. I might not see you for a while or maybe even for a long time.
Max: Well, it's time to go home. See you, Sam.
Sam: Yeah, see you tomorrow, Max.
Pat: See you around, Sam.
Sam: Oh, that's right. Today's your last day in our department. You'll be moving over to ... is it Finance?
Pat: That's right. On the 49th floor.
Sam: Well, I hope you'll come visit us now and then.
Pat: Sure will. See you around, Sam.