Are there different types of reed-beds?

Yes, there are two basic types of reed-beds - horizontal flow and vertical flow.  There are two types of horizontal flow reed-beds.

There is the Sub-Surface Flow Horizontal Flow Reed- bed (SSF-HFRB) in which the effluent flows entierely through the media and not over the top. These do not have any visible water in them. 

The other type is variously known as a Free Water Surface - Horizontal Flow Reed-bed (FWS-HFRB), a Surface Flow-Horizontal Flow Reed-bed (SF-HFRB, or HSFRB), or as an Overland Flow Horizontal Flow Reed-bed.  These reed beds are designed in the form of long shallow ponds fully planted with reeds or a variety of wetland marginal plants. They will eventually become fully vegetated.

There are now also reed-beds of both the vertical and horizontal types which are fitted with Forced Bed Aeration (FBA).