I could be wrong but doesn't the adjuster control both compression and rebound? I think there is a disc or something inside with 2 holes, one larger than the other. As the shock is compressed the volume the bottom section decreases forcing some air through a hole into the top section, The opposite on extension. Turning the adjuster on the side changes which of these 2 holes is used as air transfers between sections and hence controls the speed that air can move, ie the damping.
On a normal shock the spring and damping are separate. On an air shock the air provides both damping and the spring. It also changes thinges in a different way.
On a normal shock you can adjust the preload on the spring. By doing this you do not change the spring strength or rate, you just change where the shock sits in its stroke. Manufacturers can change the effect of this by the use of rising rate linkages etc.
On an air shock increasing the pressure increases the mass of air in the shock and effectively also increases the spring rate. You also increase the mass of air that must pass through the hole.
ie more air pressure = more damping.
This is all just educated guesswork, and applying a bit of science and mechanics, so if anyone has greater knowledge than me feel free to correct me.