"In the past quarter century semi-automatic handgun design and development has exploded. There are so many trigger mechanisms out there that it's confusing to even experienced handgunners. In this thread I'll try to cover the types, names, basic operation, and major examples of each.
We'll start with the three primary trigger mechanisms and build from there.
SA - Single Action. In this mechanism the firearm's hammer is fully cocked, and the trigger pull performs the single action of dropping the hammer to hit the firing pin and fire the round. These pistols are generally carried "cocked & locked", where the hammer is back and safety is engaged. Well known examples of this are the M1911, Browning/FN Hi-Power, some variants of the HK USP, SIG P-Series SAO pistols, CZ-75 SA, and FN FNP SA.
DA - Double Action. In this mechanism the trigger pull performs the two actions of cocking the hammer, and then releasing it to fire the round. The British often refer to DA as "Trigger Cocking" for this reason, and it helps many folks to think of DA in this way. DA autos are further split into three other categories as follows.
DA/SA - Double Action / Single Action. These pistols fire the first round Double Action, and all following shots are fired single action. They generally use a decocking lever to safely lower the hammer, but block contact with the firing pin so the chambered round is not fired.
Caution Decockers can fail, so always point the pistol in a safe direction when decocking. Decocker failures are rare in modern firearms, but do occasionally happen. Some older designs are more prone to failure. If you have any doubt that a decocker is not working properly have the firearm checked by a competent gunsmith or armorer.
DAO - Double Action Only. In these pistols the hammer always stays down, and the trigger operates only in Double Action.
Many well known brands of pistols are available in the Double Actions. Some are only available DA/SA or DAO, and many are available in either mechanism. Well known examples include SIG, H&K, CZs and Clones, Ruger, Taurus, Kel-Tec, Walther, FN, Beretta, and Smith & Wesson metal frame autos.
DAO with reduced trigger pull - These are the new breed of DA pistols, pioneered by Para Ordnace's "LDA" - Light Double Action. These pistols keep the hammer down, but cycling the slide pre-tentions the main spring / hammer spring. The result is a lighter weight DAO trigger pull, and some also provide for a shorter trigger pull & reset. Some also have the ability to revert back to a full weight DA trigger pull to give a second try if the round does not initially fire - this is known as restrike capability. Beyond Para's LDA, examples are SIG's DAK, H&K's LEM, and some Kel-Tec and Smith & Wesson Pistols. Edit: It has been brought to my attention that the hammer rests in a partially cocked position on the Kel-Tec PF-9, P-32, and P3AT; and possibly a few other pistols as well
SFA - Striker Fired Action. These pistols use a Striker, basically a hammer & firing pin in one. Most operate similarly to a lightened Double Action. Cycling the slide partially pre-cocks the striker, and the trigger pull finishes cocking the striker before releasing it to fire the round. Some pistols have the striker pre cocked only a small to moderate amount and are much like DAO in a traditional hammer & firing pin pistol. Others almost fully pre-cock the striker and are much like SA in a hammer & firing pin pistol. Others yet have striker mechanisms that are much like DA/SA. Glocks are undoubtedly the best known SFA pistols; others include Springfield Armory XD, Walther P-99 / S&W99, S&W M&P and Sigma, Taurus Millenium, Mil. Pro, 24/7, and CZ 100.
No doubt I've left some things out. If I've left any glaring omissions, or made any major or minor errors, please send me a PM and I'll edit to correct them.
If you'd like to add anything please feel free to post a follow up. If you could, please also stick with the definitions of trigger/operating mechanisms I listed above to keep things simple and avoid confusion. In your follow ups please stick to objective information and avoid being subjective. We can debate our preferences & the merits of the various mechanisms in another thread, but please keep this focused as an informative reference.
Edit 17 Jan 07: I corrected the first glaring omission I noticed and added Beretta to the major examples of DA pistols along with a couple of other tweak"
Trigger Mechanisms; A Guide to What's What - THR