Earlier quoted context omitted.
So, one wheel starts spinning, and then, at a certain speed, it gets immediately locked into the other wheel which isn't moving at all? How does that not blow up the entire differential?
With a hard-locking differential ("lockers", generally used off-road), engagement while one wheel is spinning is ill-advised. They're generally toggled on at low/zero speed by the operator in anticipation of a traction-loss situation. The variety of differential which does not immediately lock one wheel into another is http://en.wikipedia.org/wiki/Limited-slip_differential .
The type of locker I'm more familiar with takes a different approach: the rear end is locked by default but unlocks when it needs to. e.g., going around a turn causes the outside tire to turn faster than the inside one, and the teeth in the locker are angled so the speed difference causes them to cam out and decouples one axle shaft from the diff, letting it spin independently while the inner axle shaft is under power.
I had that system in my Toyota pickup and even in 2WD, it was absolutely unstoppable offroad.