The key difference between a turbocharger and a supercharger is its power supply. Something has to supply the power to run the air compressor. In a supercharger, there is a belt that connects directly to the engine. It gets its power the same way that the water pump or alternator does. A turbocharger, on the other hand, gets its power from the exhaust stream. The exhaust runs through a turbine, which in turn spins the compressor
Turbo = teh ultimate IMO, tunability for any engine with compressor sizing, boost controllers can do wonders, and they're more efficient then superchargers. If done correctly they deliver power in the entire RPM range too..
I've always been a fan of superchargers, myself, even before my first */c car purchase. Turbo lag annoys me, and very few people ever get the turbo-sizing right. They either go large for power and neglect off-idle performance, or go smaller to spool quickly, and lose upper-end. Then there'* the complicated tuning neccessary for turbos to make reliable power.
Give me a straight-forward system. I like being able to just smash the pedal down and bust off the line any old time. I don't have to worry about hitting the power band when I downshift, because the power band is the entire operating range of the motor. If I give up some mileage for it, oh well.