A little more: based on my understanding of an "open" diff, both wheels get power as long as both wheels have traction. As soon as one wheel loses traction, it gets all the power and you... lose forward thrust while one wheel spins. Back in my '60s muscle car days, we'd make fun of the guys who did the one wheel burnouts.
With a limited slip, there is either a clutch setup or a rear torsen (yes, they are used as limited slip diffs too). With the clutch setup it keeps the wheels at roughly the same speed (with some slip) when one wheel slips. Sometimes we'd test for Posi-traction (limited slip) by putting one wheel on pavement and one on the grass and then punching it. Open diff: you'd go nowhere. Posi: both wheels would spin. With a torsen I believe it actually transfers torque to the wheel with more grip (again, example is a rear diff). With either a clutch/disc based or torsen based mechanical limited slip, you'd get two stripes if you did a burnout
With too much abuse the discs wear and you eventually have what amounts to an open diff.
With braked "fake" limited slip, it's an open diff, but when that one wheel starts whizzing away (loses grip), it gets braked (single wheel braking due to the wonders of ABS tech) and then power is "forced" across the axle. In this case you'd probably melt your brakes if you tried to do a burnout.... But, it would very effectively get you off of that grassy shoulder.
