Fuji,
There is a difference between variable pitch prop and constant speed unit - it is possible to have a variable pitch prop but no constant speed unit. In that case, you set the pitch for the phase of flight - climb, cruise etc. With the simple electric or hydraulic or even manual, variable pitch prop, once set it behaves like a fixed pitch prop at that setting i.e. you speed up or advance the throttle and the RPM increases.
Moving the prop lever back and forward pre-flight checks the ability to vary the pitch and no more.
With a constant speed govenor fitted and working, having selected an RPM, the govenor will automatically vary the pitch of the propeller (within limits) inresponse to throttle movement and airspeed changes to maintain that RPM.
In order to verify that the govenor is working it is necessary to set the RPM in the governed range and vary the throttle setting slightly while confirming that the govenor responds and maintains a constant RPM.
That is why most people describe aircraft such as the C182 as having a constant speed prop as opposed to a variable pitch prop.
Regards,
DFC