Within the centersection the ring gear is bolted to some sort of differential. The differential can be open, limited slip, selectable or automatic locking, or spool style. When your 4x4 is making a turn on hard pavement, the inner and outer tires need to turn at different speeds, yet when you are off-road, you usually want the tires to be locked together so that both can help pull the vehicle through an obstacle.
Open Differentials Most axles come equipped with an open differential from the factory which delivers power to whichever tire has the least resistance by using two or four smaller pinion style "spider" gears that mesh with two side gears through which the axleshafts attach. With an open differential, if one tire is in the mud and the other is on solid ground, the tire in the mud will spin where the tire on the solid ground could pull the truck forward if it was getting power.
Limited Slip A limited-slip type differential is similar to an open differential in that it allows different rotational speeds of the tires in a corner, but when going straight it has clutches that engage, and the friction helps keep both tires turning and receiving equal torque even when one has less traction. However, if one tire has no traction and the torque input coming down the driveshaft and the traction of the tires combined is more than the friction the clutches can handle they will break loose and send power to the tire with no traction and you will go no where. In addition, limited slips often require a special additive to gear oil, and the clutches will wear out over time.
Lockers A locking differential is designed to ensure both wheels receive equal amounts of torque no matter how much traction they have, so that even if one tire is in the air the opposite one will still turn and pull the vehicle forward. There are two main styles of lockers-automatic and selectable. Automatic lockers use gears that engage when torque is applied yet still allow some difference in tire speed during cornering. Selectable lockers offer the driver the ability to lock the differential together via a cable, vacuum, airline, or electrical switch. The benefit of a selectable locker is that it acts as an open differential on the street, and then is completely lockable whenever you need it on the trail. The downfalls of this style are the possibility of damage to the activation device or plumbing, and the fact that you will need to remember to turn on the locker before you attempt an obstacle (almost every selectable-locker owner has forgotten to flip the switch on the trail once when he needed it).
Spool The most basic style of differential is a spool, though it really shouldn't even be called a differential because it never lets the wheels turn at different rates. A spool is basically a piece of steel that the ring gear bolts to and the axleshafts are splined into, but that does not have any internal gears. Spools are nice because they have very few parts to break, however they transmit an enormous amount of stress to the axleshafts when driven on the streets, and since they do not allow differences in speed during turning the tire will scrub and chirp around corners, which is harsh on tires. Plus a front axle equipped with a spool is difficult to steer, as the tires want to plow forward. Many low-budget wheelers weld the spider gears of an open differential into a solid unit, basically forming a spool that is commonly known as a Lincoln locker, referring to the welders made by Lincoln. Though we would happily put a spool in the rear of an off-road-only rig, another thing to consider is that when sidehilling in slippery mud, snow, or loose gravel terrain, having a spool or even a locked selectable locker can cause the vehicle to slide sideways, and if that sidehill is above a tall cliff, you may want to take it slowly or tie off your rig to some solid object as you move along.