Actually, aftercoolers and dryers are a little different (and the only reason I know this is because I worked on a system that had both)
The aftercooler went between the compressors and the tank, and consisted of one tube inside another, with the air running down the center tube and water running through the outer one (but I plan on building an air cooled one for mine, kinda like a little radiator with an electric fan).
The dryer was after the tank, before the filter/trap. There are two kinds that I'm aware of. A refrigerated one, that lowers the air temp even more, dropping the water into the trap, and a dessicant bed dryer that just absorbs the moisture and has to be changed every so often.
I hear now that automotive paint and body guys use disposable dessicant dryers that hook to the air hose right before the sprayer, but I have't got to play with one of those yet.
I'd start with an aftercooler. This will get most of the water to drop in the tank. Then go to a dryer if this is not enough. I think if you used a dryer with no aftercooler, you'd spend all your time emptying the trap/changing the dessicant.
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