A turbo IS a supercharger.
A long time ago, turbos were called turbo-superchargers. The nomenclature was put there to distinguish between a exhaust turbine driven centrifugal compressor, and a crank or camshaft driven centrifugal/ positive displacement compressor. Nowadays, in "street" talk (verbage of the proles), it seems to go something like this:
**Turbos-- as I explained above.
**Superchargers--crank driven centrifugal compressors.
**Blowers-- crank driven positive displacement...uhh... air movers. Air isn't compressed inside the unit so they are not as efficient as centrifugal compressors.
Turbos have had the edge in professional racing (when they are allowed) since the late sixties. They can have a much wider usable powerband than a crank driven centrifugal supercharger, and are more efficient than a blower.
Drag racing is the exception here, but that is of concern only to the worker bees in the "under classes" (sniff).