There's basically three types of superchargers used on cars. They are centrifugal, Root's and twin screw. These further break down into whether they are compressors or pumps. Compressors actually compress the air inside the blower while the pumps move air into a chamber (i.e. discharge manifold) where it is compressed. Compressor type superchargers are generally more efficient than pumps. Here's some quick info on each type of blower:
Centrifugal
The centrifugal supercharger operates generally like a turbo only that instead of using the exhaust gas to drive it, it uses a pulley and belt. Therefore it has one impeller that is driven by a belt attached to the crank. The air enters the impeller at its center and the spinning action forces the air to the outside using centrifugal force. The faster the impeller spins the higher the air pressure at the outer edge of the impeller. This makes it a compressor type supercharger. In order for a centrifugal to make boost it has to be spun relatively fast. The boost it delivers is not constant and increases as rpm increases. Boost typically starts to build in earnest at about 4,000-4,500 rpm. The bulk of the power increase from these types of superchargers occurs above 5,000 rpm.
Root's
Root's blowers are basically large capacity air pump. It take a certain volume of air and moves it from the inlet side to the discharge side of the blower case. It does not compress the air inside the blower case. It simply spins fast enough to move more air than the engine can consume. This causes the air to build up in the discharge manifold and thus boost is created. The faster the blower is spun relative to engine speed the more boost it will create in the discharge manifold. Notice that this means that a Root's blower doesn't need high rpm to make boost like a centrifugal. It can make boost right off idle and usually can make it's full rated boost by 2,000 to redline. The downside for a Root's is that because it is a pump it's inherently less efficient than a compressor type supercharger.
Twin Screw
A twin screw is somewhat a hybrid between the centrifugal and Root's superchargers. It is a compressor like a centrifugal but it delivers boost like a Root's. It uses two very finely machined screw looking rotors that inter mesh but don't actually touch each other. This makes them very efficient to drive and makes them very volumetric/thermal efficient too when compared to a Root's. They also make full rated boost from 2,000 rpm to redline just like a Root's. From the outside a twin screw looks like a Root's blower and many people mistakenly think they operate like one when this as far from the truth. A twin screw is a better supercharger the a Root's in every way you can measure except cost. Because they have to be manufactured to very tight tolerances they cost more but they are just as reliable as a Root's.