Yes, filters do indeed aid in filtration!
Airstones are mostly for looks and enjoyment. The bubbles do not significantly increase oxygen to the tank water or other gaseous exchange, but there are a couple of things they help with: If they are placed down at the substrate level, as is common, the can aid a bit in helping to lift some of the water in the lower depths up to the top, thus aiding in circulation. Also the movement of the bubbles and the action of them breaking at the surface will cause some surface movement, which will aid in gaseous exchange (the two types of gaseous exchange of most common interest to aquarists are oxygen gain (a positive thing usually) and carbon dioxide loss (a negative thing usually.))
Bottom line, despite my technical comments, is that airstones are almost entirely for looks and enjoyment.
~~waterdrop~~