Many limited slips do use clutches to try to control traction. When one tire looses traction the other side will recieve all of the torque just like in an open rear end. Limited slips use clutches, or other means, to try to harness some of that torque and apply it to the side that does have traction. There are several different designs and some are more "positive" than others but none match a true locker as a positive traction aid.
Lockers also have differences in design, but most use some type of spring loaded side plates that interlock to make a positive connection. Lockers will disengage to allow differential action, but only under certain conditions. Say you are making a turn. If you let off of the throttle, removing the torque input to the locker, the locker will be able to break free allowing differential action. Some like the lock-rite will do so with a loud bang and a noticable lurch from the rear end, while Detroit lockers do so more smoothly. If in the middle of your turn you were to nail the throttle, the locker would engage and you would very likely feel a bit of understeer and hear the tires chirp.
Think of them this way, a LS is normally open and tries to "lock" if needed while a locker is normally locked and opens only under certain conditions. There is a huge difference in the amount of traction offered by the two.
For instance, when I am rockcrawling it is very common for one of my front tires to come completely off the ground (sometimes measurable in feet). With a limited slip, even a very positive limited slip, the tire that is in the air will be getting all of the power. No LS made will be able to turn the tire that is on the ground, the difference in load will be too much for the clutches to make up. With a locker up front both tires still recieve torque and the tire that is on the ground is able to contribute to forward progress. This is an extreme example, but it does help to show the differencce between the two.