The biological filter in a saltwater aquarium is nothing more than a place for bacteria to grow. Any surface in an aquarium which comes in contact with tank water and the nitrobacter & nitrosomona bacteria species that you created when you cycled the tank is part of your bilogical filter. The velocity of the water passing over the bacteria also affects the efficiency of the biological. The faster the water moves over the bacteria, the more efficient it is, up to the point where the bacteria is being stripped from the filter surface.
The efficiency (strength) of a biological filter is determined by its surface area and the amount of water passing over it. Some filter medium are more efficient than others. Aquarium glass surface area aside, here are the most popular biological filtration methods:
Live Sand / Jaubert Systems are also very popular with many reef aquarists.
Live Rock / Berlin Systems are the filters of choice for many SW aquarium purists.
Wet / Dry Trickle Filters were the next step after the UGF to dramatically improve efficiency.
Canister Style Filters come in many different styles and sizes and can also be multifunctional.
Undergravel Filters are among the first biological filters created for SW aquarium hobbyists.
Sump/Refugium are ver popular adding water volume and natural filtration and a safe haven for natural food.
Protein skimmers, ozone units, UV sterilizers, powerheads, fluidized beds, macro algae's all can be forms of filtration.
And the thing is that you can have a mix and match of any of these forms of filtration.
I personally have liverock, livesand, wet/dry, protien skimmer. I have a canister filter but almost never use it. I occationally add the use of an ozone unit.
I would also reccomend the book The Conscientious Marine Aquarist by Fenner as your first book to lean by.
Thomas
Oh and welcome to the board