trigger performs TWO actions.
#1 cocking the hammer
#2 releasing the sear
This is a description of a single mode of action, the "self cocking" action, and is in itself double action. The term "double action" means the the action has TWO modes, manually cocked, and self cocked. This was the usage for many many years until recent times. Using the oxymoron "double action only" leads to the sort of confusion we have at present. How do we distinguish between a single action, a self cocking action, and a double action? Now add the triple action and we have a really confusing mess. I realize that in the last few years the term "double action only" has come in to usage and the language does change over time, but "change" does not automatically mean better, especially when it's a change that leads to confusion.
Dig up a few old gun books and see what they were called.
The "triple action" has three modes of operation, a single action has one mode of operation, it's only being consistant to say a double action has two modes of operation. Such was the meaning for many many years and still should be. What people have taken to calling a "double action only" was for many many years known as a self cocking action. It's only within the last twenty years that or so that I can recall hearing the term "double action only". I Before that time I never heard it applied to the self cocking revolver.
It probably doesn't help that the old single action revolvers are so called. While they are "single actions" it adds to the confusion because people don't stop to think that a self cocking revolver is also a single action.
Then there are actions like the glock, in which the striker is half cocked when the slide cycles. This is a single action that is a hybrid between manually cocked and self cocked.
Then there is the triple action. Three modes of operation. Makes it pretty clear that "single", "double", or "triple" must refer to the number of modes of operation. With a triple action in the third mode, the trigger does not cock the action.