A double-set trigger uses two triggers. Pulling the rear one "sets" the front one, and pulling the front one fires the gun. Once the front trigger is "set", the pull is measured in ounces. If you do not "set" the front trigger by pulling the rear trigger first, the front trigger fires normally, with a (usually) 4 or 5 pound pull.
A single-set trigger uses one trigger. If you wish, you just shoot it normally, by pulling rearward. It will fire with a (usually) 4 or 5 pound pull. To "set" it, however, you push it forward until it clicks. Then it has a pull measured in ounces.
I have never heard of a gun with two triggers, that if you did not set the rear trigger, the front trigger would not fire. I think you are confused.
There was also at least one shotgun out there, that had what appeared to be another trigger, but pulling it caused the shotgun to break open. There was also at least one revolver that had, apparently, two triggers. Pulling the rear trigger fired it as a double action revolver. Pulling the front trigger cocked it, and you then pulled the rear trigger to fire it. So that would be kinda like a double set trigger on a revolver.
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