Fungisal.  Greywater  (or ...

Fungisal.  Greywater  (or graywater if you are an American) is typically defined as drainage from baths, showers, lavatories and laundry - where the soaps and detergents give the water a typically "grey" colour.  In some cases kitchen sink and dischwasher drainage  may also be considered greywater versus "blackwater" from toilets and urinals (i.e. sanitary sources).  I think you are referring to drainage from precipitation, which is often separated into two groups: 1)  drainage collected from elevated surfaces and roofs - "harvested rainwater"; and 2) drainage collected from ground surfaces, walkways, and road surfaces - "stormwater runoff".  Rainwater collected or harvested from elevated or surfaces are generally considered to have fewer sources of contamination than stormwater that has been collected after flowing over the ground or paved surfaces.   How you collect the water and the degree and method of treatment you apply  depends on the expected or potential level of contamination and the quality of the water required for the  application or use.  Rainwater harvested from roof areas is often drained into above ground or below ground storage tanks that can be made of any material that holds water without contaminating it.  Storage allows suspended solids to settle, and the water cane be used for either potable or non-potable applications - depending on the treatment provided.  Potable water treatment typically involves two-stage filtration followed by disinfection, as a minimum, but often includes granular activated carbon filtration to remove any metals or organic contaminants that may be present.  Treatment for non-potable applications - such as toilet/urinal flushing, vehicle washing, irrigation, laundry, etc. - generally involves filtration to prevent sedimentation and clogging of irrigation lines.  Stormwater is often collected in ponds, or other surface containment structures, and treatment also depends on the degree of contamination and the water use.  Collected stormwater may also be  a source of water for potable use following treatment, but the level of treatment is usually greater than for harvested rainwater.  Like water from a stream, river, or lake; stormwater treatment usually consists of a large sedimentation basin for suspended solids removal, followed by dual-media or membrane filtration - and sedimentation and /or filtration may also be chemically enhanced using coagulants and flocculants - particularly if there is a high degree of turbidity due to suspended colloidal particles. 

Returning to your reference to greywater, greywater can also be used for non-potable purposes either directly (recycled) or following treatment (reused).   Using greywater to flush toilets, for example, can be a cost effective application that achieves significant water savings and reduces wastewater flows.  Because soap and detergent is biodegradable, they will likely result in biofilm growth that will require brushing periodically.  Because of this biodegradable material, if you need to store the greywater for more than about 24 hours, the biodegradable organic contaminants need to be removed - typically by bio-oxidation, followed by sedimentation and, in some cases, filtration to remove colloidal particles and improve disinfection.  While you will find some concern expressed in the literature regarding the use of greywater for landscape irrigation, due to the effect of soaps and detergents on soil structure - if the greywater is not the sole source of water applied to the soil (i.e. if there are seasonal rainfalls that can wash out accumulated salts from the soil) there should be no concerns.

I trust the above helps.  The treatment technologies involved are very basic: 1) sedimentation to remove suspended solids; 2) aeration for biological oxidation of organic contaminants; 3) filtration to remove colloidal particles that could interfere with disinfection; 4) consideration for activated carbon filtration (for drinking water use) to remove residual organic contaminants and metals; and 5) disinfection to remove any pathogenic microorganisms that may be present (i.e. bacteria,parasites,and viruses).  The choice of treatment depends on the degree and types of contamination that may be present, and the water quality required for the desired water application/use.