It would be a snifter valve, which is very much like a Schrader valve. However it has a very weak spring that will easily open if there is a vacuum. When you put a valve cap on for protection, you make sure it is not one with a seal. Tire valve caps seal, and in fact the cap seal is the main seal for your tires.
That snifter valve would be on the well side of of the check valve.
Typically there would be a drain valve (or a little hole) down the well a bit, and when the pump shuts off, the drain valve lets water out. The pipe gets air in it. When the pump next starts, the water coming up pushes that air up, thru the check valve, and into the "galvanized"/ "conventional" pressure tank.