Assuming the diff is OPEN, and both wheels are off the ground--
and if the driveshaft has any resistance applied to it (i.e. in gear) the speed of W1 and W2 will be the same, but rotate in opposite directions.
If the driver applies power, and if one wheel on an open diff has traction, and the other wheel has no traction, (or not enough) the wheel with no traction will spin at ABOUT twice the speed that it should.
If it is a limited slip type, like I thing Mr. Rat is talking about, he is correct as well.
I have a Quaife type diff. in one of my cars, and I'm not sure at all what happens there. Only that it almost works well.