I believe that was John's point, that we call a gun a "spool gun" or a "poppet gun" based only on the valve. Using the main valve to characterize the rest of the marker doesn't get you very far.
Buuut that said, I also feel that the difference in the fluid dynamics between how a radial seal and a face seal flow, especially at low lifts, are significant enough to warrant the distinction between spool type valve and poppet type valve. Characterizing the flow through the primary valve is what's what's important for us in paintball anyway.
Definitions of spool vs. poppet that don't account for the type of seal at the primary valve miss the point in my view.