There are distinctly 2-types of grey water systems; those that do not treat grey water and those that do treat grey water.
a) Systems that do not treat grey water are used for garden irrigation only. These are diversion systems where wastewater from baths, showers, basins (not kitchen sink) and washing machines is diverted to a partially submerged chamber. From here it is pumped to the garden automatically to either drip pipe or low-pressure sprayers. The filtration used in these systems is normally a basket type filter to remove larger particles.
b) Systems that do treat grey water are used for flushing toilets, laundry washing, pool top-up and garden irrigation. The treatment used in these systems would include digestion (of the grey water bacteria) and either UV-sterilisation or membrane filtration. Although these systems are more versatile the cost is usually far greater than the simple diversion system for garden irrigation. See Hydraloop and Aqualoop treatment systems.