open diffrential: most comon, found in almost all cars and trucks. allowes wheels to spin at different speeds, this is also the one where if one wheel is stuck, the other will spin lika mad in the other direction.
limited slip, posi: a happy midle ground between full locked and open. basically this unit always keeps a little power to the stuck wheel, assistin in traction, but not as nice for turning. (when you turn, one the outside wheel travels faster then the inside wheel)
lockers: brands include detriot and arb. this unit keeps full power on both wheel no matter what. used alot in off roading, and drag racing. turning is all but impossible with locked diffs.
if you need more info hit www.howstuffworks.com
and do a search.
hope it helped!