noise
Sounds like the ring and pinion, under acceleration loads the drive side of the ring gear teeth are in contact with the pinion, under deceleration back side of the teeth are in contact with the pinion.
If the diffs never been apart, sounds like there's ware goin on on the drive side of the ring gear. Remove the cover to inspect, if all looks good, wash the gears off with carb-clean, apply white grease to a few ring gear teeth and rotate a wheel once to see the contact pattern of the pinion on the ring gear teeth, should be right in the middle.