Check the stickies at the top of the page. I can give you a brief description of the different filtration types though. First is mechanical, which simply filters out solid particles. In an AC, that will be the sponge.
Then there is chemical which removes...chemicals. That is the activated carbon. Chemical isn't really neccessary, unless you need to remove medicine, tannins, etc from the water.
Then the most important is biological filtration. Thats the biomax stuff in an AC. The media has lots of surface area, which bacteria colonize. These bacteria convert ammonia, which comes from fish waste, uneaten food, or anything else thats decaying, into nitrite. Ammonia and Nitrite are very toxic to fish. Different bacteria convert the nitrItes into nitrAtes, which then can be removed with water changes. You can't just add a bunch of fish as soon as the tank is setup, because it needs to cycle. You have to wait a few weeks for the bacterial colonies to grow. Adding a few hardy fish works, or you can use filter media from a tank that has been running and is cycled already.
Mechanical filter media needs to be rinsed out and replaced every month or so, depending on how much of a mess your fish make. Carbon needs to be replaced to, or it will stop working. Don't mess with the biomedia though, except rinsing it in tank water if you need to. Otherwise you can kill the bacteria.
If you have an AC 50, thats plenty of filtration. You may be think of an air pump, not filter. The pump is to blow bubbles in the tank, which agitates the surface, and allows more gas exchange (oxygen into the water, and CO2 out) I have 2 whisper air pumps. They work fine, and are quiet enough that I don't hear it unless the cabinet is open.
A sponge filter works by pulling water through a sponge, and they work well for smaller tank
Hang-on-Back/HOB/power filters pump water out of the tank and through the media, and then the water flows back in over the little waterfall-looking part. You have a HOB.
Canisters are a lot bigger, and used mainly for large tanks. Water flows out of the tank and down into the canister, which is usually kept in the stand, where it travels through the media and is then pumped back up into the tank. They are more difficult to maintain, and more expensive.
Then there are wet/dry sump filters. A sump is a separate tank that water drains into. Water trickles over the media, which isn't fully submerged, and is then pumped back into the tank by a separate pump. They cost a lot unless you make it yourself.
here are some useful articles to read about filtration:
http://www.monsterfishkeepers.com/forums/showthread.php?t=94937
http://www.monsterfishkeepers.com/forums/showthread.php?t=88677
