An open differential drives both wheels, but if one of the wheels looses traction then ALL the torque is directed to that one wheel that is spinning. This is what the majority of cars have. These are often refered to as a 'peg leg' rear end.
A limited slip differential is one that 'limits' the amount of torque applied to only one wheel. There are several implementations that accomplish this. One is to use spring loaded clutch discs, a typical example is the Eaton differential. Another way is to use cones instead of the clutches, the example for this is the Auburn differential. Mopar's marketing name for limited slip is 'Suregrip'. And all Suregrips fall into one of these two types of limited slip. Often times these limited slip differentials are called a 'posi', but that is incorrect
Next is the locking differential. This does not use traditional clutches, it use 'cogs' to positively lock the two axles yet still allows one axle to spin faster than the other in turns. This differential is correctly refered to as a 'posi' and the example of this is the Detroit Locker.
In full blown race cars a spool replaces the differential. This solidly locks the two axles together and does not allow either side to spin faster than the opposite side.
There is also a torque biasing differential that behaves similar to a limited slip. These are more common on FWD transaxles.
And there is also an aftermarket device called a Powertrax that can be added to an open differential to make it work similar to a limited slip. The sad thing is they cost as much or more than a true limited slip. However you don't have to disturb the gears to install it so it's easy for the backyard mechanic to set up.
