Technically there are 2 types of superchargers. Positive displacement and centrifugal. Positive displacement includes screw type, roots type, and some other less common designs (like the supercharger VW used on the Corrado). Positive displacements are far less efficient than centrifugal because there is so much area that is in constant contact, meaning friction. Positive displacements also create much more heat than centrifugals. That's what I know on the subject Hopefully others will add in.