Both mean the same but 뭐니 is more colloquial (spoken) and 무엇이니 is more literary (written). *Tip: If you're texting or speaking (writing casually) *and* are speaking to your friend, opt for 뭐니. Good luck!

Yes, what SoCal Linguist said is correct. It's similar to having a root word in Arabic that can be varied and modified, and in this case, contracted. From "무엇", several different words can be derived.