Types of Differentials.
Open Differentials:
Are the most common, cheap, reliable, and provide smooth highway performance, but can get you stuck easily because power goes to the wheel on each axle that has the least traction. On a 4WD with open diffs means you can count on only 2 wheels to get any power, and they will be the ones on each axle that are slipping.
Spools:
A spool is a carrier setup that turns both wheels on an axle the same speed as the ring gear. Spools are lousy on pavement because there is no differential action, and they eat tires (especially if you ever turn corners). But you can always count on power to both wheels. Spools are common in drag racing. There's an easy way to fabricate one: Just take your open diff, and weld your spider gears to the carrier. This is often referred to as a "Lincoln Locker" because there is a good chance your welder was built by Lincoln Electric. Don't put it on the front if you ever want to steer.
Limited Slip (Positraction):
These operate mostly like an open diff, but when one wheel slips, the diff (through a series of clutches), transmits some torque to the side that is not spinning. This is a nice choice for people trucks that see a lot of pavement, but like to go off-highway once in a while and need a little help in the traction department. Limitied-slips give more traction than an open diff, but less than a locker or spool. The highway performance is like an open diff. Limited-slips eventually wear out their clutches, and use a special oil.
Lockers:
A locking differential has characteristics of both open diffs and spools. A locker behaves normally much like an open diff, but somehow (either automatically or manually, depending on the model) locks up like a spool.
The ARB Air Locker is a highly-regarded locker that is manually operated via a switch that controls compressed air that locks up the diff. When it is off, the diff behaves exactly like an open diff. When you press the switch, you have a spool and its awesome traction. This diff is expensive and hard to install, but having manual control is very nice for a rig that spends time both on and off the pavement.
Automatic lockers operate on a 'ratcheting' principle. Neither wheel on the axle can turn slower than the ring gear, but they can turn faster. Automatic lockers take some getting used to when turning - the inside wheel powers your truck around the corner, while the outside wheel is 'freewheeling'. With an open diff, the outside wheel does the powering. Automatic lockers are cheaper than the air locker and provide the same traction, though there is some ratcheting noise and wheel hop on the freeway. They can cause some spooky steering on slippery surfaces. Because of this, a lot of people don't suggest using them in the front axle.
The inside of a Locker