A double action pistol, be it a revolver or autoloader, will fire the gun regardless of condition with a pull of the trigger.
A single action pistion, be it revolver or autoloader, requires the operator to manually "cock" the action, before a pull of the trigger will result in a discharge.
In a DA autoloader, if you load a mag and rack the slide, it has already been "cocked" from DA to SA. So now every pull of the trigger will result in a discharge, the slide goes rearward and recocks the pistol. However, most DAs are equipped with a de-cocker, which puts the hammer down safely. In this condition it would be truly a double action trigger pull, as you pull the trigger the hammer will move rearward, as you reach the trigger stop the hammer falls, discharges the round, slide goes rearward, upon re-entry to battery the hammer remains back and trigger in a single action state for the next round.
In a SA autoloader, when you load a mag and rack the slide, the hammer is cocked and trigger is back and hammer is on the sear. When the trigger is pulled, round is discharged, slide goes rearward, cocking the hammer again. With an SA autoloader, if you load the mag and rack the slide, and then let the hammer down, in this type of pistol the hammer must be cocked for the trigger to pull and fire the round.
In a Double Action revolver, once you load the cylinder with 6(or capacity, or however you feel like loading) you close the cylinder. Right now the pistol is safe, trigger is forward, and hammer is down. You can pull the trigger and as you pull the trigger the hammer will go back, the cylinder will spin, and once past the sear the hammer will fall and round will discharge. Hammer remains down and trigger goes back forward once you release it. Upon another trigger pull the hammer goes rearward, the cylinder rotates, once past the sear the hammer falls and discharges a round. Now the trigger is again forward and the hammer down. At this point you could fire it "single action" by pulling the hammer back, the cylinder will turn, and the hammer will lock and rest against the sear. The trigger will now be back, more like a SA trigger. Once you pull the trigger, the hammer will fall and the round will discharge. The trigger will still go forward, and the hammer will remain down.
In a single action revolver, once you have it loaded, the trigger will be forward and the hammer will be down. If you try to pull the trigger in this condition the trigger will not operate the action. You have to manually pull the hammer back, the trigger will move rearward, the cylinder will rotate, and the hammer will rest on the sear. Once you pull the trigger the hammer will fall, the round will discharge and once you release the trigger it will again move forward. At this point again the only way to operate the action is to pull the hammer back, this continues until you have fired all 6 rounds.
I apologize if this is hard to read or offends anyone. It just seems you are mixing a couple ideas. Basically a DA you can pull the trigger and fire, a SA you have to cock to fire. I hope this helps