Those aren't the only options, you know.
Or rather, trigger type should be defined more carefully. Observing Internet Gunboard yammer about this over the years, I see different people use the terminology in different ways.
A lot of people seem to think the whole double action/single action distinction has to do with the interaction of a trigger with a hammer, and doesn't apply to guns without a hammer (striker fired). These folks make up other classifications for striker fired guns.
Others (like myself) read the SA/DA/SAO distinction to be about the trigger only, and what actions it performs. Does it only drop the hammer (or striker)? Single action. Does it cock the gun as well, bringing the hammer (or striker) up from a full rest position before releasing the sear? Double Action. Does it
have to bring the hammer (or striker) up from rest, each and every time? DAO. There are examples of each in both striker and hammer equipped guns.
And some guns don't fit the distinctions well. Glock -- striker is under a certain amount of tension at rest. If you pull the trigger and release the striker on an empty chamber, it's dead. You must manually cycle the slide before you can attempt to fire again. Is it single action? No. Double Action? No. DAO? Certainly not. Glocks are a "
Safe Action(R)". Its own thing, albeit widely copied these days.
What's on me right now? Snubby with a DAO hammer. I may in a little bit put on a Springfield XD*, with what is (to my mind) a single action trigger.
I'm fairly agnostic about it at this point, CCW having only just recently become an option in this state.
-----edit to add---
*I had some guy (on a Internet gunboard, of course) once try to tell me the XD was "just like a Glock", because the process of releasing the sear from the striker in the XD cams the striker back a fraction of a millimeter.
"Uhhhh. No."
(I didn't bother arguing with him.)