I have found one of the more confusion aspects of guns is what defines the trigger action, and I confused this a lot at first but now feel I have a good understanding of what makes a gun Single Action Only, Double Action Only or Single and Double Action.
Your best bet is to watch my attached YouTube video as it not only describes trigger actions but also has the added benefit of the visual examples of each type of trigger action.
Here is a very quick explanation of what constitutes each type of trigger action:
First off the action is based on the role of the trigger in how it effects the action, not how the slide or the hammer can effect the action of the gun.
A Single Action Only gun does one action (a single action) and that is generally the releasing of the hammer or striker or what have you... Single Action Only guns can not fire without first manually pre-cocking the external hammer or manually pulling the slide or charging handle back first to chamber a round and also pre-cock the action of the gun. Keep in mind that the blowback of the slide or bolt in semi and full auto guns effectively cocks the action of the gun allowing for single action trigger release.
A Double Action Only gun performs dual functions, the pre-cocking of the hammer or striker in the first stage and the releasing of the hammer or striker in the second stage, therefore performing two actions. Double Action Only guns do not have the ability to pre-cock the hammer or striker fully and therefore generally have a heavier trigger pull as the first stage of the trigger is to cock the sprung hammer or internal action.
Single and Double Action guns have the ability to do both, meaning they can be pre-cocked and then fired or fired without pre-cocking simply by pulling the trigger.
Keep in mind that there are some guns that fall in to their own category, take for example the Glock. Glock has been known to actually describer their guns as Double Action Only, when in fact they can not be fired without the slide first being pulled back to partially pre-cock the internal striker - similar to a single action gun. But when you pull the trigger on a Glock you do not simply release the action but rather the trigger first pulls the striker action back the final stage in order to release it, similar to a double action gun.
Again, watch my YouTube video as I hope the visuals will help you to understand the differences between Single Action Only, Double Action Only and Single and Double Action trigger.