The basics of filtering are pretty much the same in all types and from there we are often better is we fine tune that to meet what each tank needs.
Step one in thinking is why we might use each type, mechanical for straining the debris we want to hide out of sight, bio for giving a definite place for the good bacteria to line and then maybe some type os chemical like carbon, purigen, etc. but often not needed.
If we put the bio stuff with tiny pores for the bacteria to live at the start, it tends to just get the holes filled with debris which then kills the bacteria, so we usually want to do the straining first on something which is easy to pull out, flush off and replace. That lets it catch stuff like leaves, plant bits and food. How course to make it depends on what's in your tank floating around. A tank with lots of dying plants may stop up a sponge if the pores are too small but if there is not that much to strain out, a finere sponge may get down to doing smaller filtering right away. So we get to choose, big strainer which doesn't need cleaned as often or finer for catching smaller stuff.
Sometimes two stages of straining works good before passing to the bio. Big pores catch big stuff while finer catches what passes through the first but before it clogs the bio.
Bio in amounts and choices to meet eh fish load and tank situation. A new tank that needs lots of good spaces for bacteria may need more bio media if it has a big fish load than an older tank that has bacteria already built up on all surfaces or with a small fish load. I consider most any slick surface to have some bacteria and often reduce the bio media after things get all loaded with bacteria and if Have a heavy load of debris which needs better mechanical. Finally lots of folks like to have a final "polishing" type that may make the output water a bit clearer. Something like a bonded filter floss can work good for this.