These are just typical expressions we say when we give someone something. No need to analyse them.

Peachy is right. We even sometimes say "Here you are" but we don't mean it literally.

This slipped my mind when I first answered. When handing something to someone, you can use either one. In other cases, they have different meanings. "There you go" You can also use this phrase to tell someone they got something correct or give someone praise. For example: A: I can't figure out this math problem. B: You can do it. A: No, I can't. B: Well, try. A: Okay. I think the answer is 35. B: See, there you go! I knew you could do it! It's used here to add emphasis to the fact that person A got the answer correct (on their own). In regard to the second phrase "here you go," it could also be used in a different way. It can be used to show annoyance at someone. Usually when someone repeatedly does an action that annoys you. It could be someone nagging at you, or asking you for money, etc. For example: A: I know I've borrowed money from you a million times already but I promise this is the last I'll ask... B: Ah, here you go (again).... A: Can I borrow 20 bucks? B: No. The "here you go" in this case is used because person B already knows what person A is going to say and is annoyed by it. I hope this makes sense.