What is the difference between "nice to see you" and "nice to meet you"?
Are they the same or not?
They are different, "nice to see you" implies that you have already met or seen the person before. "Nice to meet you" means that it is your first time being introduced to that person.
Another phrase that is commonly used is "Nice to see you again". It is interchangeable with "Nice to see you".
You normally only say "Nice to meet you" the first time you encounter someone. You might reasonably say something like "It was nice to meet [up with] my brother again, after not having seen him for years", but you certainly wouldn't have greeted him with "Nice to meet you [again]".
But "Nice to see you" has no such "first time" connotations. In fact I'd go so far as to say that because meet has such strong associations as given above, discarding it in favour of see actually carries the implicature that you've met the person before.