Single and Double action mean somewhat different things in Revolvers and in Pistols. This was always my main confusion in my younger days too!
Remember, the "action" in single or double has to do with the TRIGGER FUNCTION.....ask yourself "what does the trigger do?"
A Single-action revolver must have the hammer c0cked manually, then the trigger only releases the hammer (hence, the "single" action)
A Double-action revolver, the trigger serves a 'double' function of c0cking the hammer and releasing it. Two functions of the trigger.
Pistols are different and more confusing.
In a Single-action pistol only the first shot must be manually c0cked, then the trigger performs the single function of releasing the hammer. THEN....the semi-auto action automatically c0cks the hammer again, then only a single action by the trigger, etc.
In a Double-action pistol, the trigger can c0ck the hammer and release it. However from the second shot, the hammer has already been cocked by the action, so it's really single-action from that point forward. So it's really "Double-action, Single-action" or DA/SA.
Now, some untrained and inexperienced police officers had a problem with that, in that the trigger pull changed from first shot to second shot (DA/SA) and they shot a second and third shot without realizing it. So the "Double-Action Only" (DAO) semi-auto pistol was developed, which requires a full double action trigger action and pull with every round.