When you say "give up", it means you can't do anything about something or you have lost interestand maybe just forget about it. "give in" on the other hand, means you cannot ressist something, or you can't do anything about it so you just follow or go with the flow.

In these lyrics they kind of mean the same thing. When he says I wanna give up he means he wants to stop trying or stop fighting for something as he says in the next line. He wants to quit. He kind of means the same thing when he says I want to give in (in this case). If these were 2 separate unrelated sentence though they can have different meanings. If i said: I want to give up. That would mean I want to quit. That I want to stop trying. If I said: I want to give in. That could mean I want quit resiting an urge to do something. Like I want to give into a temptation to do something like cheat on a diet.