The Chairborne Rangers who select firearms for large departments (or even small ones) are leery of Single Action firearms....
SO, manufacturers try....
The M&P's are nominally SA, but there's no current "code" for it, so DAO or something like "Safe Action" is used....
One of the funniest is, IMHO, Para Ordnance's LDA guns. "Light Double Action". In truth, they're as Single Action as anybody else's 1911, except that the trigger
does move the hammer back to firing position like a DA gun. Problem is that it's about 2# to get to the firing position (with the usual 5#-ish trigger), so there's little real value
except if you're transitioning to an LDA from a wheelgun.
But the Para guns don't look as aggressive
.... The hammer is down.... (Now that Para's using a very flat hammer in their LDA guns, you can use Condition One leather - a top strap under the hammer - with the LDA's. You just put the top strap over the hammer. Convenient....)
Couple of other definitions: SA/DA (or "Traditional" DA), where the first shot can be SA or DA, depending on the user's preferences. (I.e., cock the hammer if you want to.) DAO (Double Action Only) just presumes that you can't cock the hammer manually. Both of these may have double-strike capabilities. (The Para LDA's DO NOT.) Just me, but a second strike may be a waste of time in modern ammunition....
Buy several of each!
Regards,