In a previous discussion I mentioned that different LSDs influence the behaviour of a vehicle into and out of a corner (as well as their capability off road), so let's discuss a few different types of LSD.
To quickly recap, a differential connects an input shaft (power) to two output shafts (axles or driveshafts). Often those output shafts need to rotate at different speeds.
If a diff is open, those two output shafts can act independently, so (with a wheel in the air) one could take all the input shaft's power and the other could be stationary.
A locked diff allows no such differential between the two output shafts; they always rotate at the same rate. They're fine in a straight line (or getting unstuck off road), but the downsides in a rear diff are a greater likelihood of understeer, and they're more prone to lift-off oversteer. And in a front-wheel drive a locked diff is just plain nasty to drive.
An LSD solves this by being somewhere in between those two extremes of open and locked, but there are many designs. Here are some mechanical (non-electronic) types.
CONE-TYPE
Typically found in the sporty Falcons, Commodores and Aussie-made Skylines.
A cone is splined (connected directly) to each axle (output shaft) and it rubs against the inside of the inner diff casing, with a set of spider gears between the two cones (most open diffs also use spider gears). Unless you get silly with too many preload shims during a rebuild, these will smoothly transfer some torque to the wheel with the most traction without any of a locked diff's downsides.
These do wear however, and deposit fine metal in the diff oil. They need a particular oil to be used and changed periodically.
CLUTCH-TYPE
Instead of cones on either side of the spider gears, there are little clutches, and then a mechanism (possibly a cam design) applies a force to determine how strongly they rub against each other to limit the difference between axle speeds.
These are more easily adjustable (during assembly) with different ramp rates for applying the force pushing the clutches together.
In the aftermarket these are often categorised as 1-way, 1.5-way and 2-way. 1-way means they're an LSD for acceleration, but act open for slowing down. 2-way means the LSD action is similarly-strong for acceleration and deceleration. 1.5-way just means there's noticeably less of a limiting effect for deceleration than there is for acceleration.
TORQUE-BIASING
These use a set of helical (worm) gears. They multiply the torque from the side with the least grip to that with the most, but they act like an open diff if one side has zero traction (zero times any number is still zero). However, some aftermarket manufacturers have added a mechanism to apply some load if one wheel has no traction at all.
Torque-biasing diffs can mostly be found in upmarket European models in the front or rear, plus they're available from the aftermarket for many front or rear applications.
VISCOUS
Whereas the above designs are torque-sensitive (responding to the difference in torque being applied to each axle), the viscous is speed sensitive, responding to the speed difference between the two axles.
Common in Japanese performance cars from the '80s to '00s, instead of clutches rubbing each other, there's a sealed two-part chamber with plates inside, and between the plates is a viscous fluid. The outer part of this sealed chamber is connected to the engine (via the crownwheel and pinion), and the two inner parts are connected to each axle.
However, once the fluid deteriorates (from heat or high km) they behave like an open diff, and they're factory sealed so they're meant to be replaced, not rebuilt.
LOCKER
Not actually an LSD. When one axle turns faster than the other, a locking mechanism engages to lock the axles in synch. They disengage upon deceleration to be open again.
While they're suitable for the rear of off-roaders, they are brutal in fast vehicles, either failing to engage because one axle accelerates too fast for the mechanism, or fatiguing axles into failure because of the stress from repeated sudden engagements.
