Limited slip differentials and locking differentials are two different kinds of critters: the limited slip kind have clutch packs inside the differential with a certain amount of preload augmented by various mechanical tricks to increase the tension under load. These help a lot, but some of the cheaper designs, such as Ford's old Equa-Lok, will still slip a lot (and burn the little clutches out) if you try a burn out with one wheel on asphalt and one on gravel. Old GM Positraction was the best of the lot, I must admit.

The true lockers, like Porsche ZF differentials or the Detroit Locker I had installed on my old autocross '64 1/2 Mustang 35 years ago when it became clear that the Equa-Lok couldn't handle the task, use various ratcheting tricks or one way clutches (like SAAB freewheeling devices), and they really will transfer all the power to the tire with the traction, until something else breaks.

And then there are the Torsen type units, with funny little worm-gear tricks which I won't attempt to explain without pictorial capability.