These guys pretty much wrapped it up.
An "automatic" is any firearm that automatically loads the next round once fired. "Semi-automatic" will load a single round for every pull of the trigger. A true "fully automatic" firearm will continue to load and fire for as long as the trigger is depressed and rounds remain in the magazine (or belt). "Select fire" refers to firearms which have the ability to do either. The AK for example has a setting on the selector switch for semi-automatic fire as well as another setting for automatic fire.
Different mechanisms exist for cycling a firearm's operating mechanism. Most rifles are gas operated. Most handguns are recoil operated. However, some recoil operated rifles, such as the CETME/HK G3, and other HK roller locks, exist, as well as gas operated handguns, like the Magnum Research Desert Eagle.
In terms of gas operation, you have three main categories; direct gas impingement, short stroke piston, and long stroke piston. In the direct gas impingement (DGI), gas is blown directly through a small port and down a small tube into the bolt carrier group, which is then blown back to facilitate operation. This system is used mostly in the M16 series rifle. The short stroke piston system directs gas through a port into a tube where it pushes a short piston back. This either makes contact with an operating rod, as in the case of the SKS or M1A, or strikes the bolt carrier assembly itself as in the M1 Carbine. The kinetic energy from this transfer pushes the bolt carrier assembly backwards to facilitate operation. In long stroke operation, the gas is diverted through a port into a tube, where it strikes a large piston, which is attached directly to the bolt carrier group of the firearm. As the piston is driven backwards by the gas, it carries the bolt carrier with it, facilitating operation. This system is seen in the AK and the M1 Garand.