I use the terms equally. I am not certain but I believe that cooler is really meant for fluid and not air to run thru it so it is not designed for using the way most of us use it. A true air cooler unit would be more like a "heat exchanging unit like HVACs use to limit the loss of air temp when bringing in cold outside air in the winter.
I did another thing with my “after cooler/transmission cooler”: I set it at about a 45 degree angle. The air comes in at the top. At no point is there an upward turned leg that could trap any moisture.
I also have five self drain water collectors: three that I added at low points, one in the plasma cutter and one in the refrigerated drying unit. None of them have ever shown any moisture (don’t know if that is a good sign or a bad sign!)
Great stuff, thanks for sharing all the detail. So here’s what I’m thinking. I run a 3/4" maxline air system. I’ll integrate the aftercooler into that setup (likely after extending the run so it has more time to cool) and use the following fittings to connect the aftercooler to my Maxline system: https://cdn.zappy.app/5ff2e541f3eeef6efd8422c99a3b4262.png
So it will go from the tank, to 20-30ft run of maxline, through the aftercooler (which I’ll wall mount at a 45 degree angle, with a fan), then to a water trap, then it will integrate into my existing setup of filter, 1 gallon dessicant dryer, motor guard filter and then into the plasma.
Ill see how this was to remove water and then consider adding the harbor freight air dryer in the future.
@rjpowell9 all great advice in helping you get going. On the lighter side we are all like real ugly wives. We try to get as deep in your wallet as we can.
The wife to me today when I placed the Amazon order for all those parts “Does every one, like does every one have this problem with compressed air??”. Me back to the wife “Yes, all my buds in the forum, they all have the same problem, you should come see some of their ideas, it’s wild”. Her back to me “You lost me at buds in the forum” and then she walked away.
four years ago she agreed to let me buy a harbor freight welder for $165 so that I could build an offset smoker. Fast forward to now, there is a 400 sq ft shop in the back yard with tens of thousands of money into it and still no offset smoker… surprised I’m not forced to sleep in said shop…
just an update, i got the parts in for the aftercooler and automatic tank drain valve, hoping to get it installed within the next couple days and retest my cuts (to see if I can eliminate the bevel).
My son’s travel baseball schedule has been crushing me, very little time to work in the shop.
…won’t get into our wallets??? 
