Superchargers differ significantly from turbochargers, however, in that they are not driven by the engine's exhaust gases. Instead, a supercharger is typically mechanically driven by the engine. In most instances, the drive takes the form of a pulley and belt arrangement.
One of the most common types of supercharger is the 'Roots', which features a pair of counter-rotating meshing rotors. Air is drawn in, trapped in voids surrounding the lobes on the rotors, then forced out of the supercharger - at a higher rate than it is being consumed by the engine - to generate boost pressure.
Centrifugal superchargers, on the other hand, use an impeller wheel that is driven by a fixed- or variable-ratio gearbox. Typically, centrifugal superchargers resemble turbochargers in appearance - but, instead of an exhaust-driven turbine, they feature an obvious mechanical drive.
Both the Roots and twin-screw types are 'positive displacement' superchargers, which pump the same amount of air each revolution - regardless of how quickly they are being turned. Centrifugal superchargers, however, are 'dynamic'. This is because they build pressure by accelerating, then slowing the induced air - trading its increased velocity for pressure. Consequently, their output varies with speed.
You may encounter 'turbosuperchargers', but this is simply what turbochargers were often called when they rose to prominence in military applications during World War II. Superchargers were in use prior to that date, however; early concepts began to appear from the mid-1800s onwards, while the first production automotive superchargers were previewed in the Mercedes 6/20 hp and 10/35 hp of 1921.
There are several advantages to using a supercharger instead of a turbocharger. They tend to respond much more quickly to demands, particularly at lower engine speeds, and do so in a more consistent, predictable fashion. Supercharger installations also tend to be less complicated.
Predictably, there are some downsides. Superchargers can be less efficient, particularly at higher boost levels, and they require power to operate - negating some of the performance improvements.