Mechanical media is the simplest of all and it works based on the direct principal whereby larger sized molecules will not be able to pass through a certain holes or barrier and thus trapped in between. The filter media is often measured by pore size and generally the finer it is the better for it to trap free moving particles. However, there is always a certain working limit you might want to take into consideration here because too fine pore size will actually get clogged up easily and restrict movements or flow of aquarium water. Mechanical tank filter media is often used combined with multiple layers of different materials starting with the larger pore sized on top and moving further downwards to the bottom, the media pore size gets even finer. Surface area is also another consideration you might want to take into account here and basically most commonly used mechanical tank filter media available in the market are like sponge, foam block, polyester floss/fiber and scour pad.
Biological filter media generally works on the principal whereby its main purpose is to provide wide surface area for growth of beneficial bacteria. It actually encourages and provides a place for these bacteria to populate, as it will help to breakdown large toxic waste into less harmful chemical. As opposed to common myth saying that the bacteria live in anaerobic environment, this is actually not true because nitrifying bacteria relies on oxygen rich water for growth and if the biological tank filter media ever get clogged up, accumulated waste will lead to anaerobic condition and will kill them instead. Therefore when you are using these type of materials for your home aquarium, make sure that the filter media is periodically rinsed to ensure it is not clogged up but at the same time, leave some sticky waste attached so that bacteria will again repopulate. Some of the most popular and widely accepted aquarium filter media based on this biological removal concept are bio-balls, ceramic rings and canister media.
Finally, the most expensive and somewhat risky option is the Chemical filter media. Usually carbon pouch, chemical gels and phosphate pads are the most commonly available options for aquarium filter based on the chemical filtration principle. These materials offer the same capability just like biological media does on removal of ammonia, nitrite and nitrates. To certain extent, most of the time, chemical pads are only used for the sole purpose of removing fish medication that you’ve added in earlier for treatment of disease or else, I would not recommend to using these types of chemical aquarium tank filter media mainly because of cost related issues. Other than that, based on my own experience certain cheap carbon pouch brands are also known to alter the pH value of the water and thus you also taking the risk of affecting the health of your fish and therefore more time to readjust back the pH balance.