Two main types of LSD have been generally used - mechanical (geared or clutch-based) and fluid based (viscous). The latter is gaining ground especially in modern all-wheel drive vehicles, and generally requires less maintenance than the mechanical type.
In the mechanical clutch type, differential velocity is detected by some means, such as a centrifugal weighted rotor, and this applies a force to a clutch mechanism which links the two shaft together to a varying extent - the greater the differential velocity, the more force is applied. This forms a negative feedback loop which limits the slip to a preset degree. In some designs, the clutch is self-actuating. Often, small multi-plate clutches are used. One disadvantage of the mechanical type is that the limiting action tends to occur quite rapidly rather than gradually, and this in itself can create unsettling dynamic effects for the vehicle as a whole.
Another type of mechanical LSD is the geared torque-sensitive type. This arrangement uses planetary gears to "sense" torque on one shaft. The most famous version is the Torsen differential invented by Vernon Gleasman in 1958, then sold to Gleason Corporation, who started marketing it in 1982. But there are many other types available as well. Geared LSDs are less prone to wear than the clutch type, but their torque distribution characteristics can be less than ideal.
The viscous type is generally simpler, and relies on the properties of a dilatant fluid - that is, one which thickens when subject to shear. Silicone-based oils are often used. Here, a chamber of fluid rotates with the normal motion of the output shafts, but a differential motion causes paddles or vanes to move through the fluid. The greater the speed of the vanes, the more resistance the fluid will put up to oppose this motion. In contrast to the mechanical type, the limiting action is much softer and more proportional to the slip, so for the average driver is generally much easier to cope with.
Viscous LSDs are less efficient than mechanical types, that is, they "lose" some power. However, they are less prone to breakdown as long as the fluid is changed regularly.
In the 1950's and 1960's many manufacturers began to apply brand names to their LSD units. The most famous of these was Chevrolet's "Positraction". Since then, Positraction (often shortened to "positrac" or merely "posi") has become a genericized trademark for LSD's.
Other factory names for LSD's include
Ford: Equa-Lock and Trac-Lok
American Motors Corporation: Twin-Grip
Mopar: Sure Grip