whowey, I can understand what your worries are with a 16 year old and the truck with an axle like that. But, how do you trust her to drive the truck and not run over cars? Simple, you taught her how to drive and you observed how she drives. This is just one more part of that training for how to drive. The same can be said about driving a high power car or even an underpowered Geo Metro. Every vehicle has different characteristics and the driver must know and understand them.
As for your question about knowing the differences between the various types of lockers, here you go, here is a short and sweet summation of the different types of traction control out there. This is not manufacturer specific, so, use this information to understand how the systems work and then learn what each vehicle that you have is equipped with.
Open differential: The most basic of differentials. Power comes in via the drive shaft, goes to a ring gear and then through a gear assembly, applies power to the wheel that is spinning the fastest. If both wheels are spinning at the same rate, then it will apply power fairly equally. But, once a wheel starts to slip, all the power gets transferred to the slipping wheel, resulting in complete loss of traction.
LImited Slip: As the name implies, it limits the slip between the two wheels. This is normally done through a small gear assembly and a clutch pack. When both wheels are spinning at the same rate, the clutch plates are barely touching (ie, not being squeezed together) and like an open differential, most of the power is going to 1 wheel. As the powered wheel starts to slip, the gear assembly starts applying pressure to the clutch assembly. This causes the speed difference between the wheels to be limited since some of the power going to the slipping wheel is now being forced over to the non-slipping wheel. As the power is being transferred and the spinning wheel is being robbed of power (and being slowed down), the clutches will engage more and less, resulting in a vibration/chatter. The harshness of the chatter is directly related to how much traction the non-slipping tire has and how much gas is being used.
Locker: These come in a few different flavors. You have full time lockers, cable selectable (you route a pull cable to where you want to activate the locker from), electronic selectable (uses a solenoid to engage the locker), and then you have air lockers (uses compressed air to engage the locker). On the selectable lockers, they have 2 different modes they can run in, open differential (see above) and locked. When locked, both wheels are physically locked together and forced to spin at the same rate. So, as one wheel is loosing traction, the power is seamlessly transferred to the wheel with traction. The locked differential is perpetually in the locked mode. This system is great for low traction conditions or when running on a surface that gives a lot (dirt/gravel roads). But, on dry pavement, this system (when locked) can lead to high stress loads on the drivetrain while turning as you are now forcing the tires to spin at the same rate when they are actually spinning at different rates. This normally results in the locked axle "hopping" as the tires are breaking traction to keep them spinning at the same rate. If the tires do not hop, then this can lead to axle breakage or other driveline problems.
Trac-loc: While this is a brand name, the concept needs to be explained. This is a differential that automatically goes between an open differential and a locked differential. It is essentially a limited slip differential on steroids. It allows for a small amount of slip (like a limited slip). But, when it senses too much slip, it engages and becomes a locked differential. This engagement can be rather harsh if done under load. This gives a bigger one time bump than the limited slip vibrations, but once locked, it is locked. This bump transfers a lot of force to the non-slipping wheel and can lead to it breaking loose during engagement.
Computer controlled traction: Every manufacturer has a name for this type of system. This is normally what is found in cars and the higher end luxury trucks. The system works by having a wheel speed sensor in each wheel. A computer then monitors each wheel to make sure that it is spinning at the same rate as the other 3. When a wheel is sensed to be slipping, the spinning wheel is controlled by applying the brake caliper to the slipping wheel and/or limiting the engine's power. When 2 or more wheels are slipping, normally the engine's power is limited to keep the vehicle controllable. This system is sometimes used in conjunction with one of the above lockers to provide a more seamless system that does not rely on limiting engine power.
As always, if you want more info, just ask. This is a big picture view and did not go into the specifics of how each brand does the job. They all have a twist on the same idea to make the "bigger, better mouse trap". As you can see, each one has pros and cons. The question then becomes, what is the best system for what you need?