It is difficult to wrap your head around how a common differential in a car works. It's not difficult to understand because there are a lot of parts, it is because every part in the assembly is moving relative to something else. For instance, to understand how a differential is working when you go around a tight corner or when you spin a wheel on ice, you have to mentally "sit" on one of the gears and imagine what the other gears, axles and case are doing from your specific vantage point.
This is a great animation of how a Torque-Sensing differential works. A Torsen differential. It uses worm gears and worm wheels so that the power from your engine always goes to the wheel with the most gripe. So, you wouldn't spin just one wheel on ice, the power would go to the wheel not on ice, or you would spin both. I like this gear train because it's not much more complicated than a traditional differential. It doesn't use shims, wedges, clutch plates or hydraulics to pull off what it is supposed to do.
So, to my earlier point, I find it interesting to try to "sit" on one part of the gear train and try to think of what is happening to all the other parts around me. Why when one wheel is slipping does the power get transferred? What if one wheel is completely off of the ground? Does it still work? What if you applied this mechanism to something else like a ratchet system? Could you change two linear inputs of different strokes into a rotational output? Am I a geek?