Faucets with compression valves are almost always made with separate hot and cold valves. What distinguishes a compression valve from other types is that it will have a rubber washer at its base that compresses against a valve seat to shut off the water. Often this action of the washer compressing against the valve seat can be felt as a slight increase in turning resistance as you shut off the water. Faucets with Ball-type valves are found on single handle faucets. Typically, a ball valves action is like a car stick shift only with left and right motions controlling the hot and cold and front and back to control the flow.
Repair involves replacing the rubber parts, which are typically sold in kits.
Sometimes you may need more than a repair kit as some moving parts that not included in repair kits, such as the ball, can also cause leaks from wear. Faucets with cartridge type valves are available in both single and double handle styles. The double handle styles operate just like compression valves with the exception that the action is completely consistent with no need to apply any extra pressure when closing the valve as you do sometimes with compression valves. The action for single handle faucets resembles that of ball valves except that the flow is controlled by raising or lowering the handle, instead of pushing it front or back. Repair of these valves involves replacing the entire cartridge.