A torque converter lock-up I believe means the fins in the TC lock together and the trans becomes "like" a manual in a single gear where the engine is driving the gears directly through the input shaft versus when the TC is unlocked, it uses fluid pressure to drive the input shaft, which drives the gears.
Everyone already nailed the limited slip diff (LSD) definition.
It should be noted that LSD is different from a locking rear which can be electronic, mechanical/air, or inertia-lock (G80 rear end from GM) where the diff locks the rear wheels together when slippage is sensed. It unlocks at a predefined speed or when both wheels have traction. These are different from a "spool" --it was common in early racing to weld the rear spindles together inside an open differential so that both wheels were driving the car, which is important in hard cornering, especially if you've got one wheel off the ground.
So, there's OPEN, Limited Slip, Locking, and a Spool. You now have the fundamentals to imagine the different types of differentials and how they work
Oh, last thing...Chrysler also developed a neat feature for the open differentials on the base Wrangler. Whereas the high-rent models like the Rubicon come with manual locking front/rear diffs, the base wrangler has open differentials front and rear. It means the rig is effectively two-wheel drive (one front, one rear), making it almost useless in technical 4-wheeling.
So, because Wranglers already come with EBD (electronic brake force distribution), they made an additional feature called "Brake-lock differential". It's an open differential. When one wheel slips, as sensed by the traction control system, it can use the electronic braking module to apply the brake fully at the slipping wheel so that the open diff transfers power to the wheel that has traction. It's an ingenious idea, and basically added programming to equipment that's already on the rig since the module is used by the stability/traction programs. There's debate whether Limited Slip or Brake Lock is more useful in slick situations or technical 4-wheeling.