Originally Posted by Mike@GTM

Since the supercharger is driven by the belt, the rpm of the supercharger is dictated by engine rpm regardless of throttle position. Therefore, at small throttle angles, the supercharger is trying to push air into the engine against the throttle. Since the bypass valve operates on the differential pressure between the intake manifold and the pressure in the pipe, it will be open when the manifold is seeing vacuum while the pipe is pressurized. This condition will occur at idle and at low throttle angles. Once the throttle is opened enough, the manifold will see pressure and so will the pipe. In that case, the bypass valve will close since the differential pressure will not be high enough to overcome the spring inside the bypass valve.

A turbocharger's rpm, however, is dictated by exhaust flow. At low rpm and/or low throttle angles, there is insufficient exhaust gas flow to spin the turbocharger fast enough to develop boost. Therefore, the pressure in the charge pipe will not be significantly higher than the pressure in the intake manifold and the bypass valve will remain closed.

I hope that clears things up for you.