I could have sworn an open diff has one tire rotating while the other does not vs a limited slip where one tire rotates and the other either rotates the same direction or the opposite...when the engine is off.
In an LSD both wheels are mechanically connected via clutches (cone, plate or otherwise) or through a gear mechanism (Torsen). In any case, if the driveshaft is free to rotate, an LSD car will have both wheels turn in the same direction when one is turned by hand. An open-differential car may or may not (you may see both turn in the same direction, only one turn or one turn in the opposite direction) which has to do with friction, gear oil viscosity etc.
If you lock the driveshaft (e.g. put the transmission in the 1st gear position) and tried this again, you'd find that when turning one wheel by hand the other will turn in the opposite direction. In an LSD car you'd find a considerable resistance to the rotation -- the driveshaft is locked so you're working against the limited slip preload friction -- but the other wheel would also turn in the opposite direction.
The only difference between an LSD and an open differential is the
degree to which the two axles are tied together. They both have differential action. Compare this to a spool, where both wheels get equal torque and always spin in the same direction but have no differential action so the tires scrub (and the car can be downright scary) in corners.
For instance, if the wheels spin in opposite directions while the engine is off, this means that when the car is running (engine and trans spinning), both wheels will have power (and both will spin in the same direction) although one will have less power than the other. An open diff has only one wheel spinning at all times (engine on or off). Correct me if I'm wrong but I could have sworn that's how it works.
Nope. An open differential car will theoretically transmit power to both wheels under ideal traction conditions. Torque is transmitted to both axles from the differential case via the cross shaft, spider and side gears. It's just that this mechanism is apt to take the easy way out and just have the spider gears "walk around" the side gears under conditions where both tires have differing traction. When conditions aren't ideal, the tire with the least amount of traction gets the torque. If an open-LSD car has one tire on ice and the other on a prepped drag surface, the ice-wheel will spin all day and the car won't go anywhere. This can even be affected by suspension loading and drivetrain torque reactions (which is why many cars spin the same tire in a straight line...)
In an LSD car both wheels get torque, up to a point. The traction difference in a straight line or around certain corners is basically less than the torque bias tying the two axles together so you get a "
two wheel peel." But when you go around corners, you get the wheels spinning at different speeds. Under conditions like this it's still possible to get a "one wheel peel" even with an LSD.
The LSD is just distributing the torque to both wheels more evenly than an open diff. A car with an LSD in that ice/prepped surface scenario would move -- albeit slowly -- from a stop.