The location of these two mechanisms is different. The flywheel is known to be located between the clutch and the engine. The main goal of this is to make sure that the fluctuation of the energy coming from the engine will be reduced. There is a need for constant energy to ensure that the engine will work properly.
The governor, on the other hand, is used so that the amount of fuel that will be controlled. The amount of fuel that will be given to the engine will depend on the power that is being used up by the engine and the speed of the machine. The flywheel is also known to be constantly working while the machine is being used while the governor is usually intermittent.