In general, it’s the same meaning. “What will you get for me?” could also mean you’re getting something on my behalf or at my request though.

Pretty much the same but "for me" could possibly be seen as you are asking for something more than the other "get me". For example, if you going to the grocery store I could ask "What will you get for me?" from the store where I could be wondering "What will you get me?" for my birthday. This is just my view though on this question hope it helps.

Both are the same. ☺️