Hmm - that is a rotten exam question - the difference is quite subtle. My dictionary even defines to skid as to slide! I guess I would say the car slid across the ice - sliding has a sense of smooth, continuous movement across a smooth, slick surface. You (or a vehicle) would slide on ice, or an oily, slick surface. A skid usually refers to a vehicle sliding across a road or gravel surface. Vehicles leave skid marks in accidents, where the driver brakes, but the car continues to move - often sideways. Skids occur in a vehicle, or on a bicycle, where the driver brakes, in an attempt to stop but the forward momentum keeps the vehicle moving for a while longer. You will often read the expression, 'skidded to a halt'. Hope that helps.

"Skid" usually means some friction.

Slid is the past tense of slide. Skid has multiple uses, but one is that it is a verb itself. When I ride my motorcycle slowly, I skid my boots along the ground. Yesterday my boots skid along the ground. Tomorrow they will skid too. Other uses are skid marks. The residue left by objects skidding against each other. And this is a slang term as well that you might learn the meaning of one day. Skid is a noun as well. A piece of wood or other material specifically for sliding a heavy object along.