2003 Jeep Grand Cherokee limited

I think you are on the right track, sounds are from front and rear differentials. If your Jeep has a "Quadra-Drive" system, it has locking front and rear differentials. They struggle making real sharp turns on real dry surfaces (too much traction...no tire slippage). It may even leave black tire marks on dry cement roadways. The Quadra-Drive badge can be seen on the shifter console and on the left side of the rear hatch. It is very desirable option in deep snow as it is nearly impossible to get stuck. But try to avoid sharp turns on dry roads as this strains the drive train and wears tires.