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The on/off is an actuator. The tank contains the valve which is almost exclusively a poppet valve. The solenoid is itself a pilot valve. All the other components in the gun amalgamate to actuate one final valve which is the one that fires the ball. So, they're support systems and have noting to do with the air release valve's categorization.
I agree with Ydna's technical definitions for the most part. Sure, include all the actuation stuff, but once you get to the air release valve then call it correctly. Call the axe whatever you want in front of "poppet" for the air release valve and we're good. Flow sensing poppet, direct acting poppet, etc. All good enough.
FTR, I actually do design guns as a circuit. It helps me visualize the system as a whole better than staring at physical geometry. I think of gun dynamics very much in terms of how you'd write ladder logic. I am an industrial engineer by education and it kind of rubbed off.