DAO - double action only (Like a revolver).
With these, you'd normally insert a loaded mag, then rack the slide; this puts a round in the chamber, and the hammer will follow the slide down. These normally take a 6-8 pound pull for each shot. Examples include the Beretta 92/96 D models, the S&W 5946, the Para LDA, and others.
DA/SA - double action for the first shot and then single action for the remainder.
With these, you'd normally insert a loaded mag, then rack the slide, and this leaves you with a cocked pistol with a loaded chamber. To put that pistol in a safe condition so you can holster/carry it, there'll be some form of hammer-drop safety or decocking lever that blocks the firing pin and lowers the hammer to the "ready" position. First shot on these will be 6-8 pounds, then the slide will #### the hammer after each shot, leaving you with a 2-4 pound pull. Examples include the Beretta 92/96, the Sig 226/228 and copies thereof, the CZ-75, etc.
SAO - single action only
With these, you'd normally insert a loaded mag, then rack the slide, and this leaves you with a cocked pistol with a loaded chamber. To put that pistol in a safe condition so you can holster/carry it, there'll be one or more manual and automatic safeties. Examples include the Colt 1911 and copies, the Browning Hi-Power and copies, the Luger, etc.
"Safe action"
Glock's term for their DAO mechanism, where the internal striker isn't fully cocked each time the slide cycles, and the striker has to be fully cocked then released by the action of the trigger bar for each shot. In the XD/HS2000, the striker is fully cocked by the slide cycling each time a shot is fired, but several internal automatic safeties are deactivated as the trigger is pulled for each shot.