Open diff - TQ is transfered to the wheel with the LEAST traction. There is no locking action whatsoever. You see this when you get all over the gas and only one wheel spins. It lost traction and so all the power is being diverted to that side. This is what is in the V6 Mustangs.
Limited Slip diff - These have a clutch type arrangment (ours use a clutch, others may be a cone type posi) inside so that power is evenly distributed to both wheels until the differential bias is achieved. At that point, the diff will transfer any extra TQ to the wheel with less traction. This usually creates a lot of heat in the diff and causes the clutch to slip. Therefore, in a very short time, the clutch will act as an open diff until it reengages and cools down. This is an example of preload vs. bias ratio. Our limited slips have decent preload but no bias ratio. Think of it like a guy who can bench press 500 lbs, but only once. He has good strength but no endurance. These are what we have in the V8 Mustangs, known as a traclock.
Locked diff - Locked diffs transfer power to both wheels equally regardless of how much power is applied. They will continue to do this until sideloads are imposed on the diff, indicating a turn. Also known as a locker, these act as a spool while driving straight but disengage and act like an open diff while turning. Most lock much easier than unlock and so are typically seen in cars whose main goal is straightline traction (drag cars).
An example of this would be the Detroit locker, probably the most famous locker out there (and rightfully so). It works very well in the straightline, but tends to be pretty noisy and ratchety in turns as it attempts to disengage.
Another example would be the air locker, which uses a small air compressor to manually lock the diff solid. It will remain in this configuration, regardless of straightline driving or cornering until the diff is manually unlocked, usually done by flipping a switch. In that configuration, it is basically a spool.
Spooled diff - A spool locks the rear end solid. It transfers power to both wheels equally regardless of turning, straightline, TQ input, etc. It is bar none the best diff for the drag strip but a miserable experience on the street. With a spool, both tires will ALWAYS turn the same amount and in the same direction. The only exception to this is if you break an axle. And even then, that little stub of an axle in there will be turning with the wheel that's still being driven.
Another point to mention is that with lockers and spools, it's easier to break axles. Even with a stock mustang, a spool and slicks can kill an axle shaft if abused.