Standard "open" differential" is what you have, most likely... It's the "spider gears" that cause the other wheel to turn, in the opposite direction... Count the bolts on your cover, 10 or 12 bolts if it's 1/2 ton... It will have 6 lug nuts to hold the wheel on. 14 bolts if a 3/4 or 1 ton rear, 8 lug nuts for the wheel... Use a high quality 85/95 weight gear lube and fill to the bottom of the filler hole...
When you open the case, literal "muck" may come out. That's the old fluid mixing with condensation over the years, unless the vehicle traveled through water deeper than the axle, then it may have sucked water through the vent...
Check this too! Replace the vent hose if cracked and make sure it mounts up above the axle and not dragging. You can use RTV in place of an actual gasket. Apply a 1/4 inch bead around the cover and bolt holes, Torque to about 12 ft/lbs, in a criss-cross pattern, let cure overnight and you're good to go... I change my rear diff. fluid yearly, BUT normal use shouldn't require service more than every 2 or 3 years...
While you're in there check for abnormal or excessive wear on the ring gear and spider gears. You'll see 4 small gears mounted inside the ring gear carrier, these are the spider gears. Nice sharp edges and no chips, should mean it's in good condition... Check to see if the carrier is excessively loose by trying to wiggle it with a long, heavy screwdriver... Although excessive wear will make itself known to you by vibration... So FEEL the rear with your butt!
Good luck!
