Here's how you can tell:

The most obvious sign is the presence of a big orange sticker on the side of the differential that says VLSD.

Another way to find out is to lift both drive wheels completely off the ground.

With transmission in neutral, spin one wheel by hand and the other spins the same direction. Both should spin very freely.

With transmission in gear (driveshaft fixed), the wheel is much more difficult to spin, plus the other wheel rotates in the OPPOSITE direction.

With one wheel fixed (someone holding it in this case, could also be on the ground), either in neutral or in gear, it is very difficult to turn the other side at all, but it will turn given enough force.

Yet another way to tell if your 240sx (S14 only) has a VLSD (US-market S13's weren't equipped with VLSD):

Find the car's identification plate on the firewall, passenger side.

Check digit 18 in the model # (not the VIN!).

For Feb '94 - July '95: A, C, or E, = LSD

F, or "-" = NO LSD

For July '95 - July '96: A, C, or F = LSD

B, D, or "-" = NO LSD

Okay, while we're on the subject of differentials, whats the difference between posi-traction, and limited slip, any others?

Pretty much "posi-trac" and limited slip are the same. Posi-traction is Chevy's name for a limited slip diff. Like Bandaid, and Kleenex, the name takes on a generic meaning: a "Posi-" rear end is a limited slip unit.
There are others such as open rear ends, locking differentials, and spools. Posi-trac means that both tires are spinning almost all the time. The differential (this is where the limited-slip comes in) has a clutch in it. When both tires get to spinning very quickly (as in loss of traction), the differential transfers the power to the tire with the most traction. Hence the limited slip name. Good example? Say you have a 240 with about 350 hp. Limited Slip diff. You wind it up to about 5g, and side-step the clutch. What do you get? A lot of wheelspin, and two black marks for a while. However, if it keeps on spinning, the differential will sense the loss of traction, and disengage the clutch to whichever side has the least traction. Say the left side is hooking up a hair better than the right side -- it transfers the power to that side so that the left side is pulling, and the right side is just rolling.

Open differentials are just that. Both tires are free to spin whichever way they want. However, one tire (usually the right) is the driving wheel. That's where all the traction goes. If you wind it up and dump it, and just one black mark appears, chances are you have an open differential, or you are riding a motorcycle.

Locking differentials are pretty cool. There are three types -- speed-sensitive, torque-sensitive, and a Detroit Locker. From the way I understand it, a speed-sensitive diff just spins the right tire, but if it senses that it's spinning way too fast, it will "lock-up" the other tire. So for example, if you wind it up and let it go again, the right tire will spin (one black mark) for a few feet, and then the diff will realize that there's a loss of traction (the car is not speeding up quite as quick as what the wheel is turning), and it will engage the other axle. Torque-sensing acts pretty much the same way. A Detroit Locker acts kinda opposite. It's almost always locked together, meaning it's driving both tires. However, when you go into a curve, and one axle is turning faster than the other, it will unlock and start clicking. (They are extremely noisy.) When you exit the turn, it will lock back up and start turning both tires again. They're kinda dangerous in the sense that when they lock-up, if you're not totally out of the curve, they will create some nasty understeer. Lastly is the spool, or "welded" diff. You've heard of people welding the axles together, well here ya go. Pretty much the axles are locked together 100% of the time. This is only good for drag racing, or driving in a straight line. You can't take a curve effectively because one axle is not free to turn faster than the other one, causing you to "hop" around a curve.

Now, for the MOST FREQUENTLY-ASKED question!

I have a 240sx without a VLSD and would like to have one put in.

Solution:

Get a differential from a wrecked 240sx with a LSD (see above for how to identify) and the back half of the driveshaft from your model 240sx S13 or S14 and replace the parts on your car with these. You can also use a VLSD from a J30, but you'll have to grab the axles as well - the J30 differential has different bolt patterns on the axles and won't work with your 240sx axles. Be sure to replace the gear oil in the pumpkin with new oil.