I have no idea why or how some got to calling an XD single action. It's a striker fired pistol, LE agencies considering just like a Glock, M&P, etc.
Some agencies consider it to be like a Glock, but not all agencies. And certainly not all federal agencies. The BATF considers the XD to be a single-action weapon, as does IDPA, which makes forces it to compete in the Enhanced Service Pistol Division in their matches.
Originally, the "action" described what happened when you pulled the trigger, and I'd argue that the presence or absence of a hammer is sort of irrelevant.
Note: I spent so much time trying to phrase this properly, that I'm repeating some things already posted.
There are guns that are:
1)
single action, where some other action, such as hand-cocking or slide movement charges the hammer spring or striker spring, and the trigger simply releases that stored energy by letting the hammer or the striker go... The XD falls into this category, along with 1911s, BHPs, and a lot of other guns, including the old striker-fired LUGERs! (I've had a couple of those, and they had GREAT triggers!)
2)
double action, where pulling the trigger cocks/charges the hammer/striker spring and also releases the hammer or the striker. I had a CZ-100 that was a true double-action striker-fired gun, and a Sphinx 2000 that was a true double-action ONLY hammer-fired gun.
3)
semi-double action (or Safe Action, or modified Double-Action) in which slide movement is used to partially charge the hammer/striker spring, with the trigger pull adding extra force to the process. Pulling on through released the now fully charged springs to drop a hammer/ release a striker. Glocks do this, as do some S&W semi-autos, like the 4043 I once had: pulling the trigger wouldn't do anything unless there was a modest amount of slide movement, first.
Maybe there should be a fourth group:
DA/SA guns (or SA/DA) are really double-action weapons that can be cocked by slide movement or by hand-cocking, like a SA gun, or worked by using ONLY the trigger, like a true DA gun. Are these guns in a class by themselves? Perhaps. They are certainly pistols with a dual nature...