AE grease - check. Smear it on the diff plates? Nooo.
The grease is there solely to lubricate the balls in the holes in the diff gear. Putting it on the diff plates attracts dirt and dust the very place it's not wanted. When the gear is driven it takes drive from the pinion to the spur gear. The spur gear pulls against the balls which in turn send drive to the axle via the diff plates.
When the car turns, the balls are pushed to one side of their hole or the other, but they also want to rotate as one wheel has a different speed to the other. The rubbing contact in the system is between the balls and their holes, nowhere else. The diff grease must be in the holes and on the balls for the diff to work effectively. It isn't needed on the diff plates because there is no movement between the balls and the diff plate.
You only need a smear of grease on each ball to have the desired effect, and minimise the dirt and dust that might stick to the diff. HTH
