it isn't so much the filter and more the media type used,
mechanical filtration uses sponges and pads to catch muck and debris as the water is forced through, a small amount of bacteria will build up but even fine sponges don't have a large surface area (otherwise the water would have difficulty flowing through), although there are carbon sponges they are not as effective as actual chemical filtration (also chemical media needs replacing/recharging monthly which would be quite costly if sponges).
chemical filtration uses media such as activated carbon and zeolite to remove chemical compounds such as chlorine (activated carbon) ammonia (zeolite, but only useful in freshwater) this is why the chemical filtration needs to be removed before any medication is used, activated carbon will also remove tanins, chemical filtration can become part of the bio-filtration if left in past it's useful life cycle so when it is then removed can damage/reduce the bio-filtration so should be replaced monthly, chemical filtration isn't used for muck/debris filtration.
biological filtration uses ceramics, rocks, plastics to house bacteria that consume/convert nitrogen compounds such as ammonia and nitrites, these ceramics etc.. have very fine pockets (bubbles) in them that give them very large surface area for bacteria to grow/colonise, bio-media isn't used for either debris collection (if debris builds up on the media then either the mechanical filtration has failed or the aquarium is way past a water change) or chemical filtration as such chemicals can do major harm to the bacteria colony (one of the reasons it's so important to dechlorinate) biological filtration can also be plants to remove nitrogen compounds.
a lot of internal filters tend to be sponge types, whether that be pump or air driven, these types removes waste but rely upon having a substrate to act as bio-media (or the bio-media used is very small) when sponges are used for bio-media tend to be quite large, hobs tend to bridge the gap between internal and external by allowing for different media types to be used but not in large capacities, with external filters large amounts of different media can be used depending on need.
another point to note is that just because a filter is supplied with a type of media doesn't mean that a different media can't be used instead.
there are other methods of filtration ie.. moving bed, flow etc.. but these aren't seen in small applications.