Electric Shower

Mains cold water supply heated by electricity.
Needs dedicated  electric cable from consumer unit (fuse box) to the shower area.  If replacing an existing electric shower the size of the cable already fitted could limit the size of the new shower.
Some people love them others can't stand them.

Pumped shower

Shower pump usually fitted on floor by hot water cylinder pumping the hot and cold supplies (gravity fed) - Giving excellent results! Storage tank needs to be large enough so as pump doesn't suck it dry.

Booster shower

Similar to pumped shower. Looks like an electric shower but has a pump inside it and sucks hot and cold gravity fed supplies into shower area.          

Venturi shower

Uses gravity fed hot water and mains pressure cold water. Ideal for some flats or houses with poor hot water pressure. Under the right conditions can give power shower performance without the need for a pump.

Mixer valve  

If used on gravity fed hot and cold supplies the performance is only as good as the head of water available. If used with combi boilers or unvented systems, exellent results can be achieved, due to mains pressure cold water and almost mains pressure hot water.