1-The Positive Displacement Pump or PD Pump
The first type of pump is based on the concept of creating or opening up a void into which liquid will flow and then moving the filled void to make room for another empty void. In this way the liquid is physically transferred from an intake point to an outlet point.
Displacement can be achieved in a number of clever ways, it could be through
1) clogs on a wheel or gears that rotate -the gear pump,
the gear pump 
the internal gear pump
3) though inter meshing gear cylinders that move fluid from one end of the cylinders to the other – the screw pump OR as in 4.
4) through rotating vanes – the rotary vane pump 
2-The Centrifugal Pump – Spinning Action
The second type of pump is based on the principle of centrifugal force whereby fluid is introduced into the centre and through a spinning armature or impeller throws the liquid away from the center. This in turn creates a negative pressure area or suction at the center which draws more fluid to it from the inlet. The liquid once thrown hits the enclosure walls and the kenetic force is transformed into pressure to drive the liquid out of the outlet.
Centrifugal Pumps come in various types you have submersible pumps, inline pumps, self-priming pumps, multistage pumps, regenerative pumps and more