Rear end question

Kickdown explained it pretty well and I'll add a bit.
The bearings that the pinion gear rides on are a tapered roller style bearing, and the amount the nut is tightened determines how much the crush sleeve is crushed down to set the preload on those bearings.
Once that preload is set, the pinion gear itself should be back in it's correct position to mesh with the ring gear correctly (and hopefully stop the noise and vibration)
Sometimes it works out fine, and sometimes it take a replacement of the bearing and crush sleeve to start fresh.
Sometimes the gears are already toast and only replacing them will solve the problem.

That's what we need to try and determine.