howstuffworks.com
no kidding, its a nifty resource.
Differentials are needed because it makes sense to have at least two drive wheels. The trouble comes in when you have to apply power to both wheels, but they have to spin at different speeds (when you go around a curve, the inside wheel does not turn as much as the outside). You could lock the two wheels together where they always spin at the same speed, but that makes it hard to turn as one of your wheels will not be rolling along the pavement very well.
Most cars have an open differential. This does not mean that only one tire drives the car. What this means is that as long as the resistance to rotate is the same for each tire, both tires will push the car equally. This is how a car with an open diff can spin two tires when there is very little resistance (wet pavement, gravel, etc..). Usually its not this way though as one tire generally gets loaded more than the other so the one without the load lets loose and keeps getting more and more power applied to it. As soon as one tire gets less resistance to spin than the other - the one with the less resistance starts getting more power applied to it. In a turn, the inside tire has the least resistance to spin. Open diffs are very noticeable here too as the inside tire will spin if you power on too quickly.
A limited slip differential is just what it says. It will limit the slip between the two tires. There are several ways to do this. The most common for imports is the Helical Gear type LSD. This is usually referred to as its marketed name TorSen (Torque Sensing). These LSD's require no rebuild and last the entire life of the car always with the ability to transfer roughly 40 percent of the power to the wheel that is getting the grip even if the other one is completely loose. The draw back is that they consume more energy to work so you available torque to the road is limited through more parasitic drag from the drivetrain. Positraction is a brand name of GM's common clutch type limited slip differential. The most common for muscle cars on the street is this clutch type. There are a series of clutches and springs inside the differential that 'mask' the resistance difference between the two tires. This allows some slip so that the tires can go at their own pace around a turn, but when you go to launch it keeps power applied to both wheels at all times. The drawback here is that in a turn the application of torque either from pressing the gas pedal or lifting the gas pedal will cause your car to steer on its own. Apply throttle usually tosses the rear to the outside, lifting will tend to make the car plow. Torsen's are king here because they behave like open differentials when you lift in a turn which is exactly what you want when you are lifting in a turn.
Then you have ratcheting LSD's. These are less common, they use a weighted ratcheting mechanism to keep one tire from spinning free of the other but allow them to rotate at different through a turn. The drawback here is all the noise they make when you go through a turn. I'm not sure, but IIRC detroit lockers may be a brandname for this type of limited slip differential.
Up next are locking differentials. These are open differentials that allow you to use air or electricity to lock the two axles together. These are common on 4x4's where on the street you don't need the tires locked together and an open will get you along a little more efficiently. When you get ready to launch, drive through some deep mud, or up a big rock (my favorite) you just hit a button and the differential goes from being completely open to being 100 percent locked together. This means that both tires will always spin at the same speed.
Then you have your spools or mini spools. They are simply devices that slip over the two axle ends in the differential and lock them together. Common for dragsters as they don't have to turn - worthless for the street because you'll be dragging a tire across the pavement whenever you turn. You can accomplish the spool type differential by welding the spider gears in an open differential together.
I think that covers the more common lsd's available for automobiles. I'm pretty sure there are some more exotic setups but these are the only ones that come to my mind.