There are three main Aquaponics systems, namely; Media based (flood and drain), DWC(Deep water culture)/Floating Raft, NFT (Nutrient Film Technique).
Media Based (flood and drain) is the most common Aquaponics system, popular with DIY and backyard systems, DWC / Raft design is used mainly in commercial situations, and NFT is the least used design in both backyards and commercial systems.
Media Based systems use gravel or expanded clay medium located in grow beds where plants are grown direct where they are sown. The grow beds are usually flooded and drained periodically, allowing water to circulate through the system on a regular basis.
DWC / Floating Raft systems are constructed with long channels which hold water at a depth of around 30-40cm depth, with boards that float on top of the water. Boards can be made from styrofoam, plastics, or anything else that you can get to float. Holes are made into the boards, and net pots are fitted. Plants are either sown directly into the net pots, or transplanted from other growing area. The plants grow with their roots always immersed in the long channel of water below the boards.
NFT systems are the least used in Aquaponics, due to its high maintenance needs, including very good mechanical filtration systems needed. Plants hang in net pots much like Deep Flow systems, but instead of a body of water always to hang into, a small amount of water is run along the base of the channel where the plants roots can access it.