The AE white diff grease has some "grit" to it to keep the diff from slipping. The black grease is used for gears and thrust washers. It is a regular type grease. Black grease on the diff will make the balls slip on the diff plates. Be sure not to get any on the diff plates against the slipper plate. It is possible for the plates to slip on the slipper plates if they have grease on them.

If you want to get real crafty you can pin the slipper plates and notch the diff rings to stop any possible plate slipping from happening.