basically. They may be a little different internally, but they do the same thing.
The idea is both wheels spin together, with a little give between them for taking tight turns.
The opposite is an open differential. If 1 wheel spins, the rear end will send 100% of it's power to that spinning wheel and the car doesn't move and you get the dreaded 1-wheel peel. WIth a limited slip, both wheels see power, so if 1 wheel starts spinning, the clutches in the differential will grab the other one and send power to the other wheel and puch the car forward (or cause that wheel to spin up).
They are not physically joined. That's a "locker". Both wheels will spin together but it makes taking turns very difficult.