Differences between fixed displacement pump and variable displacement pump?

the main difference between them is the way that energy is added to the fluid to be converted to pressure increase.

In dynamic pumps, energy is added to the fluid continuously through the rotary motion of the blades. These rotating blades raise the momentum of fluid and the momentum then is converted to pressure energy through diffuser in pump outlet.

In positive displacement pumps, the energy is added periodically to the fluid. the pump has reciprocating motion by pistons for example. When the fluid enters the pump through valves, the reciprocating piston begins to press the fluid resulting in going out of the pump with pressure rise.