Well yes and no...you refer to mechanical filtration where particulates get trapped and removed from the water. But there is also biological and sometimes chemical filtration as well. In biological filtration for example, nitrosomonas bacteria oxidize ammonia resulting in nitrites and nitrospira bacteria oxidize nitrites into nitrates. Then with chemical filtration, sometimes materials or resins are used to adsorb impurities from the water (e.g. activated carbon). Plants do an excellent job of filtering as these extract nutrients (aka pollution) from the water and convert it into plant tissue, often eventually removed through trimmings.
So filtration is more than may meet the eye.