The action of a firearm is its moving parts. There are many types of firearm actions and some subtle variations. They don't all fit neatly into categories and subcategories. I'll give it my best shot (so to speak).
A gun barrel has two ends. The end where the bullet comes out is the muzzle. The other end is the breech.
Guns use gas pressure, generated by burning a propellent (gun powder), to force the projectile (bullet) down the barrel. Obviously this pressure can't be allowed to escape out the breech.
In the early days of firearms it was technically difficult to bore blind holes in solid billets of steel, thus gun barrels were fabricated as hollow tubes, open at both ends, and a plug was fitted to the breech end of the barrel. Since these were muzzle loaders the breech plug could be permanent.
Eventually it became obvious that for a whole slew of reasons it would be better if firearms were loaded from the breech end. Accordingly the barrel and the breech block need to be separated from one another. The mechanism by which this happens is called the action.
In firearms that use self-contained metallic cartridges the breech block is not gas tight. Rather the case expands against the chamber walls to make a gas tight seal and the breech block locks the case in place.
Assault weapons do not exist. It is a term made up by those who seek to disarm us. It is generally applied to firearms that have a military look, despite the fact that their function is identical to firearms with a traditional look. See semi-automatic below.
The idea is to confuse people who have little or no experience with firearms. Talk of "assault weapons" is intended to muster support for restrictions, any kind of restrictions, on our right to keep and bear arms. Once the public is comfortable with some restrictions more will follow.
Go here for an excellent presentation on the political nature of the term "assault weapon".
Note: The last two, automatic and select fire, have been heavily regulated by federal law since 1934.
Despite what you may have heard, terrorists and psychos can't just waltz into gun stores or gun shows and leave with fully automatic weapons. Not even in Texas.
Hand guns are guns you can fire with one hand. Who would have guessed? They come in two flavors: revolvers and pistols. A revolver has a revolving cylinder which holds, most often, six cartridges, but eight and five are also common. A pistol is either: every handgun that is not a revolver, or a synonym for handgun, depending on who you ask. Most non-revolvers are semi-automatic, meaning that a portion of the energy released by the fired cartridge is used to extract the fired case, chamber a new cartridge, and often re-cock the pistol.
The most famous single action revolver is the Colt Single Action Army, or SAA for short. You will see one, or two, on the hip of almost every gun-toting character in almost every western movie or TV show ever made. What makes a single action a single action, is that the trigger performs only a single action. Get it? That action is firing the gun. The gun must be cocked by hand. If the trigger is pulled while the hammer is down (un-cocked) it will have no effect.
The most famous single action semi-auto is the Colt Model 1911. Like single action revolvers, the trigger on a single action semi-auto only fires the gun. The firing mechanism must be cocked manually to fire the first round. Some of the energy from each round will then be used to extract the empty case, chamber a new round and re-cock the pistol, making it almost instantly ready to fire the next round.
A double action revolver can be fired from the hammer-down state with a long hard pull on the trigger. In this case the trigger is performing two actions: cocking the hammer and firing the gun. Many double action revolvers can be used in the single action mode by cocking the hammer directly. This results in a much easier trigger pull and better accuracy. Double action revolvers that can't be fired in the single action mode are referred to as double action only or DAO.
Double action semi-autos can also be fired from the hammer down state. If they are capable of single action fire, then additional shots will be in the single action mode because the semi-auto mechanism will cock the pistol. Double action semi-autos that can't be fired in the single action mode are referred to as double action only or DAO.
Many small revolvers and semi-autos intended for concealed carry are DAO because this reduces the chance of an accidental discharge and because there is no need for an external hammer which can snag when being drawn.
Break action handguns are hinged such that folding the gun at the hinge exposes the chamber or cylinder for loading.
Smith and Wesson's first revolver was called a "tip-up" revolver. The barrel tipped up, the cylinder was removed for loading / unloading, then the cylinder was replaced and the barrel tipped back down.
Other revolvers were of the "top-break" design. The gun hinged forward of and below the cylinder so that the cylinder would be exposed for loading and unloading.
Long guns, as opposed to handguns, are intended to be fired with two hands, most often from the shoulder. Legally speaking, according to the National Firearms Act (NFA) of 1968, rifles must have a barrel at least 16" long and an overall length (with folding or collapsing stock extended) of at least 26". Shotguns (smooth bore) must have a barrel length of 18" and an overall length (with folding or collapsing stock extended) of at least 26". Short barreled rifles and shotguns can be owned, but to do so involves paperwork and a $200 tax.
Mention a lever action and most people envision a Winchester Model 1873. The '73 was not the first lever action, but it was the first commercially successful one. As the name implies, operating the lever ejects an empty case, cocks the rifle, and chambers a new round. Lever actions typically have tubular magazines under the barrel. The classic designs have an external hammer but many newer lever actions have no visible hammer.
A bolt action is characterized by a metal cylinder, containing the firing mechanism, located in the receiver immediately behind the chamber and operated by a handle sticking out to the right (although left-handed examples are sometimes available). A method of securing the bolt against rearward travel when fired is also required. Most often the bolt rotates on closing engaging lugs which hold it firmly in place. Lifting the bolt handle and drawing the bolt to the rear ejects a round. Pushing it forward again strips the next round from the magazine and chambers it. Rotating the bolt handle back down locks the bolt in place making the gun ready to fire. Some bolts cock on opening while others cock on closing.
The granddaddy of bolt action rifles is the model 1898 Mauser. The function of today’s bolt action rifles is not significantly different from this rifle.
A pump action works by pulling the fore-stock to the rear to open the chamber, eject the empty cartridge case, and pick up the next round from the magazine. Pushing it forward again chambers the new round. Pump actions are common on shotguns. Most often fed from tubular magazines but examples with detachable box magazines can be found.
In a break action firearm there is a hinge placed such that when the parts of the firearm are pivoted at the hinge the chamber swings clear of the breech block, exposing it for loading or unloading.
Semi-automatic long guns use part of the energy from the fired round to extract the empty case, chamber a new round and cock the firearm. The two most common systems are blowback, for low power cartridges and gas-operated for high power cartridges.
In the blowback system the bolt does not lock in place. The mass of the bolt and its spring keep the breech closed long enough to fire the round. The empty case pushing on the bolt face imparts enough force to cause the bolt to move to the rear against its spring. The spring then closes the bolt stripping and chambering the next round.
In the gas operated guns some of the high pressure gas is bled from the barrel via a port near the muzzle. This gas operates a piston of some kind to drive the bolt rearward against its spring. A cam unlocks the bolt at the beginning of this cycle and rotates it back into its locked position at the end.
As the name implies, in a falling block action the breech block drops straight down when the action is worked in order to expose the breech for loading and unloading. Falling block actions are often mechanically uncomplicated and very strong.
Many early single shot rifles had falling block actions, but examples of repeaters with falling blocks can be found as well as newly manufactured falling blocks.
Like the falling block, where the breech block falls, in a rolling block the breech block rolls, meaning it is a segment of a circular disk which rotates on a pin down and to the rear. This exposes the breech for loading and unloading. An extension of the hammer moves under the rolling block to lock it in place during firing.
Rolling blocks are very simple, fairly strong actions. They were very popular at one time. I am not aware of any that are not single shot.