Difference between flywheel and governor

Fly wheel

A flywheel is a big circular mass to store energy when in the form of rotational kinetic energy slowly added to it by intermittent torque, generally in a internal combustion engine Pistons . Once the wheel starts rotating its intertia will keep the Rytham.
To give an  anology just take a solid disk suspended on its center with frictionless support and attach a crack leaver at the center and try to rotate till it rotates at a constant speed. Then slowly the force on ur hand reduces now after the speed is reached if you try to added more force or reduce the force the wheel will not slow down or speed up quickly this way it will keep th Rytham or speed.

Governor 

A governor is basically a fuel input or energy input controller for an engine. As shown in the picture it will have two equal weights A & B hanged pivoted at on the central shaft with equal length arms. When the shaft rotates both arms tend to move up due to the centrifugal weight that acts on the weights. The movement of arms will be controlled generally by an added spring with adjustable stiffness that why the speed at which the governor shaft has to rotate is decided at equilibrium. This is bit confusing if you don't consider that the shaft only rotates when it is connected to engine shaft by some means and the speed leaver is connected to moving arms of the governor. So effectively the governor is a speed controller but it works with energy input from the engine. 


In short:

Flywheel

• Flywheel is an intracycle device
• It reduces the jerk due to fluctuations.
• Flywheel is mandatory for the machines like bike for start of operation.
• It controls the speed variations due to internal means.

Governor

• It is an inter cycle device
• It controls the speed variations due to external means
• Mandatory for devices where constant speed is desired like generator.