I am not sure if I understand your first question or not but here goes; Your axle has a differential inside it that could be either a limited slip, locker, open or the differntial could be replaced with a spool which provides no differential action. If you plan to replace your differential then you would need to replace it with a limited slip one if you still want to have the limited slip feature. Most people do not replace the differntial if it is already of the limited slip type unless they have blown it up or are getting into offroad or drag racing where the locker or spool type might be of an advantage.
As for a definition;
The differntial in your axle is there for only one reason, it allows the wheels to trun at different speeds when going around a corner. If you didn't have the differntial (as in a spool) one wheel would have to slip/scrub/chatter across the surface of the road to compensate for the miss match in speeds during a turn. This also puts tremendous amount of load on the drive train and things will break in a short period of time.
The basic open differntial allows the wheels to turn at different speeds making corners smooth and easy on the drive train action. Also, in a straight line equal amounts of torque are applied to both wheels as long as they both have equal traction. If they do not have equal traction 100% of the torque is routed to the wheel with the least amount of traction. That is why you wind up with only one wheel spinning in low traction conditions or during a burn out with the open differential.
The Limited Slip Differntial provides the same ability for the wheels to turn at different speeds when going around a corner but has the big advantage of ensuring some torque is always applied to both wheels. This is done by using clutches or other mechanical means. So what happens now going around a corner the wheels try to go at different speeds and the torque differnce between them increases to the design limit of the limited slip and they start to slip allowing the different wheel speeds. In low traction conditions both wheels will spin and during a burn out you break the wheels loose from the pavement without exceeding the required torque difference for the limited slip to slip thus both wheels spin.
Off road you you get your self into some situations where the wheels will have large differences in traction. In these situations you would wear out a typical clutch trype limtied slip quickly or may not be able to get through a tough spot. These people go for a locker, which is a differential that can be switched from open to locked via a switch in the cab. They are typical air activated.
A drag racer does not car about going around corners so they want the lightest and strongest rear end possible so a spool is used that eliminates all differntial action.
The limited slip has many designs the most common and smoothest is the clutch type which is what came from the factory in your truck. There are other designs that use a mechanical ratcheting mechanism such as the Detroit Locker or Power Trax and still others that use gears (not to be mistaken with the spider gears in the typical differential). When you hear people talk about limited slip additive it is only needed in the clutch type and allows the clutches to slide smoothly.
Hope this helps!
