What is the difference between turbocharged and supercharged engines in Audi vehicles?

I've always wondered what makes a turbocharged engine different from a supercharged one in Audi cars. Can someone explain it to me?

Turbochargers use a turbine to increase the amount of air and fuel that can be burned in the engine, while superchargers use a belt or chain to directly add more air and fuel into the cylinders.

The main difference is that turbochargers rely on exhaust gases to spin the turbine, while superchargers are powered by the engine's crankshaft.

Turbocharged engines have a slight delay or 'lag' before the power kicks in, while supercharged engines have more immediate power delivery.