..SA/DA/SAO distinction to be about the trigger only, and what actions it performs.
Put me in that camp, although I don't think we're in the same tent...
Does it only drop the hammer (or striker)? Single action. Does it cock the gun as well, bringing the hammer (or striker) up from a full rest position before releasing the sear? Double Action. Does it have to bring the hammer (or striker) up from rest, each and every time? DAO.
This is a pretty good standard, but I disagree with a small part of it. The part about "from full rest position". I don't think that matters. Of course, others disagree...
If the trigger cocks and fires the gun, it performs 2 actions. Hence Double Action. I don't see where it matters if the hammer or striker is "at rest" or "partially cocked". If you remove " bringing the hammer (or striker) up from a full rest position", from your definition, it is still accurate, and covers a wider range of designs.
GLock, apparently believes that "from full rest to full cock" is necessary to call it a double action. They make a big point of how their gun is different from that, and call their system a "safe action". I suppose its a better marketing term for them than calling it a partially preloaded double action system, but that's what it is.
I see it as a double action if the trigger does two things, cocks the gun, and fires the gun. I think calling it one name if the trigger completely cocks, then fires the gun, and another if the trigger only finishes cocking the gun, then fires it is splitting hairs.
What about SIGs? with their "standard" DA/SA system, when you decock the gun, the hammer is NOT at full rest position. Does this mean its NOT a "real" DA trigger pull? I think it is.
It matters little how you, or I define things, it seems, somewhere down the road, someone else will redefine it, and consider us both "wrong".