It is probably not helpful to take a manufacturer's name for its firing mechanism and make it into a TYPE of action. Example of "named" actions are Glock (Safe-Action) and Sprigfield (USA or Ultra Safety Assurance).
Semi-auto pistols generally have two types of actions: (1) hammer fired and (2) striker fired. There are sub-categories within each type. The distinguishing factor is whether the firearm has a hammer or not.
Examples of hammer-fired mechanisms are the Colt 1911, Browning High Power, Walther P38, S&W 39, Beretta 92, HK USP, SIG Sauer P220, Ruger P89, and similar. Some of these are SA (single action) and some are TDA (traditional double action) and some are DAO (double action only). Single action must be cocked in order to fire the weapon. TDA can be fired by the trigger, and after the first shot, subsequent shots are single action, in the sense that the hammer is left cocked until being decocked. DAO pistols are fired by trigger action, and hammer is never left cocked, instead decocking itself automatically after each shot.
Examples of striker-fired pistols are SIG Sauer 320, HK VP9, S&W M&P, Glocks, Springfield XD, and similar. In this type of pistol, the trigger engages the firing pin (striker) directly through a linkage called a trigger bar rather than by engaging and releasing a hammer to fall against the firing pin, as in the hammer fired type.
Within each type of firing mechanism, there are different operating systems.
Examples of hammer fired actions commonly referred to as DAO would be those in which the hammer returns to a fully- or partially-lowered position after each shot without separate decocking by the shooter. Specific types are the Beretta 92D, HKs with the LEM trigger, SIG Sauers with the DAK trigger, S&W 5946, 4046, 1046, 4546, etc. Within this category are some models, such as the S&Ws, in which the hammer is returned to a partially cocked position after each shot, as opposed to going to a full resting position. The partially cocked position makes the trigger pull easier, but usually does not allow a second shot without re-cycling the slide. I say usually as the HK LEM type does allow a re-strike, although with a heavier trigger pull. Other types of DAO pistols return the hammer to a fully lowered position, allowing re-strike capability. This type typically has a heavier trigger pull than the partially cocked type.
There is a similar sub-category of striker fired pistol in which the striker is left, after each shot, in a partially retracted position in order to make the trigger pull lighter. Glocks, M&Ps and XDs fit this category. Of those three, Glock's striker must be retracted further than those of the M&P and XD in order to be released to fly forward to fire a cartridge. Another sub-category of striker-fired pistol releases all striker energy returning the striker to a fully at rest position so that it is not under spring tension.
The bottom line is that NONE of these designs "go off" by themselves. I would venture a guess that more than half of all LE officers carry either a Glock or an M&P, including plain clothes officers carrying concealed. They simply don't "go off" without pulling the trigger. Are there negligent discharges? Yes, with any type. That, however, should not lead to a wholesale rejection of an otherwise fine and safe design.
On the other hand, if hundreds of thousands of officers carrying this type of pistol does not convince you of the inherent safety of the striker-fired design, or if you do not trust yourself enough to keep your finger and anything else away from the trigger by using a proper holster to cover the trigger, then by all means, carry what makes you comfortable. Or, don't carry at all.
Firearms are dangerous, and exactly NONE of them are proof against negligent handling. Thus, if a condition one (cocked and locked) single action 1911 frightens you, then use something else. If a partially (Glock) or fully (M&P and XD) cocked striker is not to your liking, then use something else. Some people are completely ok with no external safety on a revolver, but not with a pistol. Often, it is simply a misunderstanding of exactly how the firearm works and the fact that the inner workings are hidden from view more than with the visible hammer of a revolver or certain pistols. So, I always tell people that if their nerves will not allow the constant worry of carrying one type of action or another, then they should get a type with which they are comfortable.