The Whipple and KP (screw-type) superchargers compress air by rotating fins (or screws) . These sit on top of the lower intake (in place of the upper intake). The screws are rotated by a pulley and belt run with the accesory belt. Air comes in, is compressed by the screws and then forced down the lower intake. As stated, these make boost and a lot of power very early on in the power band - great for the street (think street light to street light where you don't necessarily have time nor room to wait for the rpms to increase and boost to come on).
Vortek, Paxton, ProCharger are centrifugal superchargers. These are units that compress the air by means of a turbine (rotating fan) and then it is forced through the throttle body and upper intake. Same principle as a turbo but instead of exhaust gases spinning the turbine, the motor spins it via a belt run through the accesories. These take a bit longer to "spool up" so power comes on a bit later (compared to the whipple) but goes a bit longer (into the power band).
By compressing the air and forcing it into the motor, superchargers create pressure (or boost). There are different levels. A side-effect of compressing the air is that it gets hotter (detrimental to performance) so intercoolers (or aftercoolers) can be used to lower the temperature of an intake charge (ProCharger does this very well).
With all superchargers, you have to pay very close attention to air/fuel ratio and timing. With the added pressures and temps, more fuel is required and timing will have to be backed out at upper rpms to keep the engine alive and healthy.
Also, different "trim" levels (think A-trim, S-trim, etc. for Vortek) are just different levels of boost the supercharger can create (due to different impeller sizes or designs or other factors) and accompanying complements for the kit. (ie. a 6 psi. kit vs. a 9 psi. kit vs. 14 psi. kit, etc.)
Hope this helps a bit...