re: Why do pistol manufacturers label strikee fired actions as DAO?

Just from a functional aspect, I think of them as SAO. I know there are different internal mechanics, but to me:

a SAO pistol with no safety engaged, is "cocked" (ready to fire) when you rack the slide, and pulling trigger will fire the chambered round. I mean, something will hit the primer and it will attempt to set the charge off to launch the bullet down the barrel.
If for whatever reason that chambered round does not fire (light strike, dummy round, etc), simply pulling the trigger again does not cause something to strike the primer again, in a SAO. You must recock the mechanism; with a striker fired gun you can't get to the striker, so you rack the slide. With a 1911 or Hi Power (SAO hammer fired guns), you can access the hammer, and can recock it... or you can rack the slide.

With a DA/SA gun, you can just pull the trigger again.

So in JUST MY OPINION, I consider anything that can have a second strike by just pulling the trigger, to be DA, and anything that requires additional action beyond pulling the trigger to be SA.

Going beyond that gets confusing and pointless to me, as far as function.