a supercharger is tied to the rotation of the engine so when the engine RPM rises the supercharger RPM also rises.
At the same time the engines need for air is also rising so overall a supercharger gives a relatively consistent boost over the RPM range.
A turbocharger is driven by the exhaust gasses of the engine which is why at low RPM a big turbo wont be spinning fast enough to produce any boost but at high RPM the amount of exhaust gasses rises exponentially which in turn spins the turbo faster which results in more boost which means you can inject more fuel which again results in more exhaust gasses and the cycle continues until you either hit the RPM limit of the engine or theres a point where you cant inject more fuel or the friction losses become greater than the extra boost you would get from the extra exhaust gasses.
oh and of course most high power turbo cars will have a valve to limit the boost pressure so this cycle doesnt literally blow up the engine.
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