A turbocharger uses the exhaust gases from the engine to drive a turbine, which in turn drives a compressor. The compressor then compresses the air that is fed into the engine, resulting in a greater mass of air and fuel being burned and therefore more power being produced.
A supercharger is mechanically driven by the engine, usually via a belt or chain. The supercharger compresses the air that is fed into the engine, again resulting in a greater mass of air and fuel being burned and therefore more power being produced.
In general, a turbocharger can produce more power than a supercharger, but it is also more complex and expensive to install. A supercharger is simpler and less expensive to install, but it is less efficient than a turbocharger.
Ultimately, the best choice for a particular engine depends on the specific requirements and budget.