Turbochargers are driven by exhaust gas from the engine and a Supercharger is driven normally by a belt off the crank. There are advantages and disadvanages to both. A supercharger can make power almost instantly because it is drive by the motor. Since a turbocharger is driven by exhaust gases, pressure has to build and gas velocity has to build enough to spin or spool the turbine. A supercharger takes power from the engine (known as parasidic drag) whereas a turbocharger doesn't.
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