On my high horse again, >:(there is double action and there is single action and there is even a tri-action.
1) Single action, cock it and pull the trigger it go's bang, in a semi-auto, you cock it once and the slide cocks it for you, but you pull the trigger it go's bang, but only after cocking the hammer or striker. No other way it fires.
2) Double action, there are 2 ways of making the firearm discharge, cocking it and firing, or just pulling the trigger, which cocks the hammer and fires. 2 distinct methods of discharging the round.
3) Tri-action is really a double action, you can cock the hammer, or pre-load the hammer spring against the hammer, or just pull the trigger.
4) Double action only, is a made up term, to define, shooting the firearm by pulling the trigger only, and not being able to cock the hammer manually. But since that is the only method of firing, it is by definition a single action.
5) For the term DAO, I prefer trigger cocking only.