Air couplers and plugs can be very confusing, mostly because of the fact that many different mfr's come up with their own methods of identifying them.
(to the best of my understanding):
A = Aero
M = Milton (Everyone else refers to these as "Industrial"
T = Truflate
L = Lincoln
I see that Shraeder-Bridgeport
has recently come up with a fairly good cross-reference between many of the "common" brands, including NAPA (which is really Shraeder-Bridgeport) Links to both the product catalog itself and the cross-reference charts can be found at the above hyperlink.
BTW, MOST of this product line is now under line-code NTH in Canada as well.
I also believe the terms "quick-coupler", "automatic coupler", and "push-connect coupler" to be the same thing.
Milton makes a "3-in-one" "A-M-T" coupler (#745 / 746
) that accepts most common types, including the long "Lincoln" style ... so it's really a "4-in-one"