diff fluid question

Would putting the wrong diff. fluid in a rear end cause noise’s or problems? My dad had his service done on his Jeep, and every time he moves from a start, it kinda shutters and makes funky noises. Almost sounds like a tire is rubbing, but they aren’t. He thinks they may have put fluid in for a vehicle without a limited slip, and his has one.

can put the additive in. itis good possiblity that the limited slip additive was not added