What is the difference between a turbocharger and supercharger in the Audi A3?

I have been looking at different engine options for the Audi A3 and I keep seeing options for both a turbocharged and supercharged engine. What is the difference between these two types of forced induction and how do they affect performance?

A turbocharger uses exhaust gases to power a turbine that compresses air into the engine, while a supercharger uses a belt-driven mechanism to force air into the engine. Both options can improve engine performance, but a supercharger typically provides power at lower engine speeds while a turbocharger is more effective at higher speeds.