You see the acronyms, SA, DA and SA/DA but what do they really mean and why do you care?
Let’s start by defining what they are, then talk about the advantages and disadvantages of each one.
The difference is what happens when you pull the trigger. In a double action firearm, the trigger pulls back the hammer, and then releases the hammer, causing the chambered round to fire. The trigger in a single action only releases the hammer, causing the round in the chamber to fire. In a single action/double action, the first round is double action, while remaining rounds are single action.
As we mentioned, a single action only releases the hammer (it performs one action) which generally results in a much shorter and lighter trigger pull. As you can imagine, a safety is crucial if carrying a gun in single action mode and most modern single action handguns have at least one safety.
Since a double action handgun both cocks and releases the hammer (performing two actions), its trigger pull is generally long and heavy and in most cases this is considered the safety.
Single Action / Double Action
In a single action/double action setup, the first shot fired is double action, each round after is single action. This is possible because when the first round is fired, the slide cocks the hammer, putting the firearm in single action mode. These will typically feature what is called a decocker, which will safely drop the hammer and put the firearm back in double action mode without firing a round.
Although it isn’t mentioned in the title, there is also a striker fired model, which is used by Glock, Springfield Armory, S&W and others. The trigger releases a striker instead of a hammer to allow the firing pin to ignite the chambered round.
On a Glock, the trigger performs two actions (cocking and releasing the striker) so it is a double action firearm.
With Springfield Armory XD/XDM or Smith and Wesson M&P for example, the trigger only releases the striker, (single action).
How your handgun fires makes a big difference in how it shoots. A longer, harder trigger pull may require more range time to get used to, while a short and light trigger pull may require getting used to using a safety on the draw stroke. When carrying a single action/double action, you will want to practice getting that first shot off in double action mode, then knowing how it fires in single action mode for follow up shots. There are a lot of things to consider here, but knowing the differences up front can reduce some frustration (and expense) later on.
Whichever you choose, make sure to practice with it how it will be carried to build muscle memory.