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List of possible pump_mechanism=* values.
Key Classification Value Comment
pump_mechanism Positive displacement gear Gear pump involves two or more wheels touching each other as to intake, effectively displace and then output processed fluid. It covers Lobe pump and Roots-type supercharger.
screw Screw pump involve a screw - with a continuous cavity - to move the fluid along its axis. It looks like an Archimedes' screw but have to raise the output fluid pressure to be qualified as a pump. It is not a progressive cavity pump.
progressive_cavity Progressive cavity pump is different from a screw pump as moving part is composed of discrete cavities moving around an axis. Cavities get the fluid during intake and displace it along the chamber to the output with a positive pressure.
diaphragm Diaphragm pump is often a double chamber pump than sequentially fill and empty due to a diaphragm action driven by electric or pneumatic cylinders.
peristaltic Peristaltic pump involves a flexible fluid chamber pushed by external roller which both intakes and outputs fluid outside the pump. It is most used in biomedical appliances which requires to let fluid untouched from external component.
rope Rope pump is built from a piece of rope with disks or knots attached and matching the pump chamber diameter immersed in processed fluid. Moving the rope displaces the fluid out of pump chamber with a positive pressure.
rotary_vane Rotary vane pump is composed of a rotary wheel with vanes pushing the fluid out of pump chamber. Vanes dimension can change as to match orregular pump chamber diameter or shape. This includes radial piston or flexible impeller. Such impellers don't transmit kinetic energy to processed fluid until you find a centrifugal pump (see below)
piston Piston pump involves a reciprocating moving part that sequentially sucks fluid into the pump chamber and pushes it out. It covers Plunger pump and Beam engine. It is different than a Diaphragm pump as the diaphragm doesn't plunge into the fluid and doesn't move like a piston.
Velocity centrifugal Centrifugal pump involves a high speed rotating impeller transmitting kinetic energy to processed fluid that gets its direction changed often by 90° angle from intake. This speed may be converted latter into fluid pressure while it exits the pump in the discharge pipe.
axial_flow Axial flow pumps use a high speed rotating impeller directed in the axis of the processed fluid flow. Direction of the fluid remains unchanged and the speed may be converted latter into fluid pressure depending of the discharge pipe design.
eductor_jet Eductor jet pumps may be used in water wells to push out water with the help of pressurised air injection. Most commonly known as injector this value only regards usage as pump.
Gravity ram (Hydraulic) ram uses high flowrate hydropower to deliver fluid at a higher pressure but lower flowrate than intake. Hydropower energy is converted in mechanical form with the help of gravity.
siphon Siphons may be used as pumps to deliver a small amount of fluid at a higher level than reservoir with the help of most part of the fluid as gravity driver in a closed cycle. It is quite special and not so common actually.
Impulse pulser Pulser pump requires a constant flow of water running into a closed chamber, mainly coming from upper reservoir. Intake is placed just at the surface of the reservoir and sucks air as it goes down to the chamber. Air gets trapped in the chamber and pushes a part of the water out at a higher level than input reservoir.
airlift Airlift pump takes advantage of floating air to raise level of processed fluid. Air is inserted in the outlet pipe and pushes fluid higher toward the output.

Those pump mechanisms technologies are also suitable for compressors as you may see in the Wikipedia classification.

Pump Mechanism Examples

Positive Displacement

Internal Gear Pump

To the left you can see an internal gear pump at work:

Internal gear pump
Screw Pump

To the left is a powered uncovered screw pump and to the right is a hand powered screw pump. Screw pumps may also be known as archimedes pumps.

Zoetermeer Vakgemaal De Leyens Archimedean Screw looped
Archimedische Schraube

Progressive Cavity Pump

See below for progressive cavity pump animation:

Progressive cavity pump animation

Diaphragm Pump
Peristaltic Pump

Watson-Marlow Peristaltic Pump
Peristaltic pump
Rope Pump
User of Rope Pump in Tanzania
Rope pump in Museo Nazionale Scienza e Tecnologia Leonardo da Vinci

Rotary Vane Pump
Rotary vane pump-diagram
Piston Pump

Velocity Type Pumps

Centrifugal Pump
Centrifugal Pump
Multistage centrifugal pump
Axial Flow Pump
Eductor Jet Pump
Eductor pump

Gravity Type Pumps

Ram Pump
Ram Pump
Hydraulic Ram pump - - 238476
Ram Pump (Vogn 2011) ubt
Siphon Pump

One of the pump drawn below is a siphon pump.

Hydraulics; siphon, pumps, and a beam pump. Engraving c.1861 Wellcome V0024612EL

Impulse Type Pumps

Airlift Pump

Below is shown a bubble pump, which is a type of airlift pump.

Bubble pump