though filter material hold BB(beneificial bacteria) it has to be cleaned, so when you refer to bio media you are reffering to something that house BB but does not(to any large extent) remove physical matter from the water column. heres a little explanation, hope it helps.
mechanical filteration- a physical filter that removes tangable particles out of the water such as food, poop, leaves, and junk. an example of course mechanical filteration media would be a pond filter pad, felt would be a good fine mechanical filter media.
chemical filteration- this involves using chemical reactions to clean your tank of dissolved toxins. usually activated carbon is used, the more activated just means it is the purer element of carbon. the more activated the more effective because the toxins in you water react with the carbon to form a new solid but stay in the carbon pellets itself, effectively removing it from the water. chemical media either works like this or reacts with the toxins and forms new molecules that evaporate and/or are harmless to aquatic life.
biological filteration- a media with the greatest possible surface area to house Beneficial Bacteria or BB for short. this media should never be cleaned and if it has to be, never clean it all at once, clean half once a month or so, so that you don't completely decimate you BB population, this will cause a spike in ammonia but mainly nitrites, the two main toxins BB "eat" and turn into leass harmful compounds. media in ths section includes cinders and bio balls.
does that help?