Your description of a limited slip differential (LSD) is correct. The point at which the slippage will lessen is called bias. Some LSDs have low bias, others have high bias. The lower the bias, the more mannerly the LSD will be on the street, but the less usefull it will be offroad. A high bias LSD will be more useful offroad (deep snow, dirt, sand) but may be more of a handful on slick pavement. Some LSDs are capable of having their bias adjusted.
There are basically two types of lockers: (1) Automatic, and (2) Selectable. The EZ Locker, LockRight locker, and Detroit locker are all esamples of automatic lockers. The ARB locker (pneumatically activated) and the Ox Locker (mechanically activated) are examples of selectable lockers.
All automatic lockers essentially act the same: the two axle shafts are locked together, unless one is coasting around a corner; in that case, one of the axle shafts disengages, and power is only applied to the other wheel. When the vehicle straightens out, and the tires are going the same speed again, the two axle shafts are locked together again. In some occasions, if power is applied during a turn, the two axle shafts will abruptly lock oether again - this can get squirrely on the street. Even is one axle shaft is disengaged, applying torque to only one rear wheel can cause the vehicle to swerve. Automatic lockers in the front axle don't present a problem on the street, as long as one is in 2WD and power is not applied to the fron axle. It is not necessary to unlock the front hubs if you have a front locker - it is only necessary to not apply power to the axle. This is assuming that your locker is operating correctly and unlocks one wheel when coasting in turns. If you're in 2WD, the front axle is always coasting.
Selectable lockers, on the other hand, are always either locked or unlocked, as determined by the driver.
The term "lunchbox lockers" does not refer to the operation of a locker, but refers to the construction of the locker. If a locker replaces the entire differential (except for the R&P gears), including the carrier, it is a full locker, not a lunchbox locker. All selectable lockers that I am aware of are full lockers, as the entire differential is replaced. (LSDs also replace the entire differential).
On the other hand, "lunch box" lockers only replace part of the differential. The carrier is not replaced. The EZ Locker and LockRight Locker are examples of lunchbox automtic lockers. The Detroit Locker is an axample of a non-lunchbox automtic lockers.
When lunchbox lockers are installed, they depend on the strength of the original differential carrier and other OEM differential parts for their ultimate strength. Non-lunchbox lockers are built with carriers that have increased strength designed into them. So it is generally accepted that lunchbox lockers are not as strong as full lockers. But lunchbox lockers, because they have less parts, are considerably cheaper than full lockers. They are also usually easier to install, since the R&P pre-loads don't have to be set up again.
Whether a lunchbox locker locker will be strong enough for your particular purposes is determined by, among other things: (1) The strength of the OEM differential carrier and internal parts; (2) The torque applied to the differential; (3) The size tires ddriven by that axle; and, probably most importantly (4) the driving habis of the driver. My CJ7 has lunchbox lockers in both axles, and I run 4.56 gears and 35" tires, and the engine is a warmed-up AMC 360 V8. Even in some hairy situations, I have never had a locker of axle shaft failure. But, then, I'm a believer in taking the best approach to an obsacle and then easing the Jeep over it, rather than the brute force technique.
If you're going to do a lot of serious four wheeling, especially if you have a heavy right foot, you'd do best to not use lunchbox lockers. Actually, in such situations, dual selectable lockers would probably be best. But they're a lot more expensive. For example, the locker parts for the LockRight lockers in both of my axles cost under $700. A pari of detroit lockers would probabl cost twice that. And a pair of ARB lockers, with pump, would probably cost between #1600 and $1800.
