Maybe this will help:
The power available from a supercharged engine will fall with height as it would with a normally aspirated one, because what comes out depends on what goes in. It is more accurate to say that a supercharged engine, at whatever height, will give out as much power as an unsupercharged engine of similar capacity and RPM would give at ground level. The engine’s power output increases slightly in the climb, because exhaust back pressure and inlet temperature are reducing. This increases volumetric efficiency.
Because they are internal devices, and driven by the engine, superchargers can use up a lot of power (150 HP in a Merlin) and therefore fuel, increasing costs and reducing the range of the aircraft. They must also be controlled and continually adjusted by the pilot.
Turbochargers use the engine’s spent exhaust gases to operate an automatic wastegate, so turbochargers are external exhaust-driven superchargers. In fact, the word turbocharger is a contraction of turbosupercharger.
As exhaust back pressure increases when the turbocharger's wastegate is closed, engine power reduces slightly. Engine power remains much the same up to full throttle height for that power.
Phil