Okay. So im going to explain it in the way that I understand it to be, which i assume is correct, but i may be mistaken.
Open Differential: Quite simply, it never locks, or 0% locked 100% slip. Basically the power goes to one wheel and allows the other wheel to spin freely. PROS- allows the vehicle to rotate faster around a corner which improves turn radiuses CONS-diminished stability in straight lines and can be difficult to get the power down because 100% of the power is to one wheel which has limited traction
Locking Differential/Locker: unless separately manually engaged, these are always locked, or 100% lock 0% slip. This means the power goes to both wheels equally. PROS- best possible traction under WOT (wide open throttle) and best straight line stability. CONS- can become tail-happy in less-than-ideal conditions and because locked diffs never slip, turning becomes increasingly difficult
Thats where limited slip diffs/anti-spin diffs/ anti-slip diffs/ whateveryouwanacallit diffs come in
LSD/ASD: there is a preset "setting", if you will, that determines when it locks. Lets say its 50/50 lock/slip. The diff will allow the wheels to spin up to or about 50% power, at which point it locks. PROS- slip allows it to turn while lock allows it to put power down and increase stability. CONS-might be a little touchy in the rain or snow (buts thats the best par).
All of these are mechanically based. There are also electronic diffs like in the Ford Focus RS which is basically a complex electronic traction control to allow more or less slip. I may be wrong, but im quite confident the diffs in all our trucks are mechanical