A Turbo-Supercharger is the correct name for a Turbo-Charger, or simply turbo.
A supercharger uses an impeller geared off the crankshaft to provide additional manifold inlet pressure.
Turbosuperchargers use an exhaust gas driven turbine to power an impeller, as opposed to a gearing system.
Both systems provide the ability to either increase power at low altitudes or maintain sea level rated power to higher altitudes.
TSIO-540 stands for a Turbo Supercharged Fuel Injected Horizontally Opposed 540 Cubic Inch engine.
P.S. That's a good background article for anyone doing CPL AGK.