Stock is clutch-type. Here is a quick cut and paste highlighting some of the differences:
With an open diff, torque is transferred to both wheels, with more going to the wheel spinning fastest. Since it is easier to spin a wheel that isn't gripping, that wheel gets more power applied to it, increasing any traction problems. A limited slip differential applies torque to the wheel spinning the slowest. If one wheel loses traction, power is transferred to the other wheel. A viscous limited slip differential uses a series of stacked slotted discs attached to the ends of each axle shaft, with silicon fluid between them. When one wheel loses grip, the discs coupled to that wheel will rotate quicker than the others. This causes friction between the two discs that heat up the silicon fluid. The silicon expands and pushes the discs together, locking them and transferring more power to the wheel with grip. Most stock Nissan LSD's , such as the 350Z, G35, and older Altimas (newer ones are open diff) are the viscous type. They are smooth but not as great at transferring power.
A mechanical limited slip transfers torque to the slower spinning wheel by using a spring loaded or cam actuated multi-plate clutch between the axles. Mechanical LSD's can be the most efficient LSDs but they can be noisy and rough in operation. Some Nissan trucks and Pathfinders use this sort of diff. Most aftermarket LSD's are clutch type as well. The cam actuated clutch type diffs can be classified as one way, 1.5 way and 2 way. The 1 way diffs work during acceleration. The 1.5 way diffs work slightly while the car is braking as well. A 1 way or 1.5 way works best on FWD cars or cars not used for hardcore road racing. The 2 way diffs work during acceleration and braking. Two ways work best for drag racing, hardcore road racing on high-powered cars and for drifting. The cams mounts in the differential over the pinion shafts and applies a wedging force to the clutch plates when the axles spin at different speeds. The cam profile determines if the diff is going to be a 1 way, a 1.5 way or a 2 way. The final type is the helical gear, which have longer angled teeth that can mesh two unparallel shafts. The stock 6 speed Spec-V's and Maximas, and the Quaife are of this type. These diffs use the fact that a spur gear can turn a worm gear but not vice versa, to provide the locking action. They are very smooth in operation and also have good locking capacity.
Phantom Grip, Nismo, Cusco, and Quaife all offer aftermarket limited slip differentials for the 1989-1998 240sx's for a few hundred dollars. Your other option is to replace your differential with a LSD model from another Nissan, about $300 at a junkyard. These are your easiest choices for a swap: all Canadian 240sx's and the 240sx's with Super Hicas had VLSD. You can also use the differential from a non-aspirated 1990+ 300zx- not the twin turbo version! The NA one has the same gear ratio (4.083:1) while the twin turbo one has a 3.61:1 gear ratio. One caveat- you will have to replace the output shafts on the differential so it will bolt up to the 240sx driveshaft because the bolt pattern is different. That will cost another $200-300. There are a few ways to check for the LSD's if you're looking through the junkyard. There should be an orange sticker on the differential that identifies it as an LSD. Otherwise, jack the car up, put it in gear, and spin one wheel by hand. An open diff will spin both tires freely, in opposite directions. With a VSLD, the other wheel will be more difficult to spin but spins in the same direction. This is a fairly straightforward install for most wrench monkeys but be careful- the differential is heavy! Support its weight with a jack to avoid getting crushed like a soda can beneath the tire of a semi truck. You also need to switch to LSD fluid or add an LSD additive after the install.