That truck should have a Dana 80 in it, most likely 3.55 and might not have a limited slip in it. The Dana 80, 70 and 60 all have same basic shape when looking at the cover but the D-80 will measure 13 1/2" top to bottom vs the D-70 at 12 5/8" and the D-60 at 12".
Those diesel trucks don't want to move unless both wheels are putting power to the ground, my '90 Cummins came with an open diff and it sucked trying to take off in the rain and forget about snow. If you do discover and open diff and want to upgrade, put a limited slip in it instead of locker, I have a locker in my truck and I'm not happy with the racket it makes at slow speed "no load" turns like in parking lots.
Oh and congratulations on the "new" truck, once you get used to the diesel you won't want to mess around with a gas truck ever again.
