The Merlin engine was not turbo-supercharged, that option was rejected. (See
Rolls-Royce Merlin and Griffon
) The supercharger was driven mechanically. That is by the engine via a shaft and gearing. A turbocharger, like those fitted to modern cars, is driven by the exhaust gases turning a turbine. So a turbocharger is a type of supercharger, hence turbo-supercharger, but not all superchargers are turbo-superchargers. I think there may even have been electrically driven superchargers in the past. Superchargers require much more exact engineering and so are more expensive to manufacture. Turbochargers suffer from turbo-lag. There is a delay between the engine increasing speed and the extra power being produced. However, they are easier and cheaper to manufacture so are most often used in modern car engines. VW were the only volume car manufacturer to use superchargers and they seem to have abandoned them now.
Mechanically driven superchargers require power from the engine, in the case of the Merlin several hundred hp. This is not the case with a turbocharger as the energy comes from the waste heat of the exhaust gases. However mechanically driven superchargers are able to produce much more extra hp than a turbocharger and so overall they are more powerful engines.