The main difference between a turbocharger and a supercharger is the way the charger draws power from the engine. Superchargers are usually actuated by a belt that's connected directly to the engine, while turbochargers draw power from waste gases in the exhaust system.
Each system has advantages and disadvantages. By running off front-end power, superchargers reduce the amount of energy that's available to the car's power train. Turbochargers are theoretically more efficient, as they use waste energy in the exhaust system. This arrangement causes back pressure in the exhaust system, however, and can reduce the engine's efficiency at low RPMs.