OK, Col, here you go:
In cowboy movies (the American "Old West") and in some war movies you will see guns that require a manual action before they will fire again. For instance, the German bolt-action rifle, the Old West lever-action rifle, and the classical flintlock are all non-automatic guns. Some old-style Old West revolvers require you to manually **** the hammer, which is called single-action. The Lee-Enfield rifle that was used by UK armed forces is an example of the non-automatic class, as it is a bolt-action weapon.
More recently, double-action revolvers allow you to fire up to the number of rounds in the revolver without manual cocking of the hammer. That falls into the category of semi-automatic. A semi-automatic weapon will reload or otherwise prepare itself, usually by capturing some of the recoil gasses of the weapon or absorbing the recoil of the cartridge as the power to cause that automatic reload. However, you still need to pull the trigger again to shoot it again. Holding down the trigger on a semi-auto weapon is just finger exercise. The U.S. Army's M-1 carbine (a relatively short-barrel rifle) is semi-auto. The weapon preferred by fictional hero James Bond was a Walther PPK, definitely semi-auto. Note that there is some confusion in designation, as many non-revolver pistols are called "automatic" but they are definitely semi-auto in operation.
A fully automatic weapon will reload itself, again based on recoil gas capture or spring-based recoil, but if you continue to hold down the trigger, it will fire again and will keep on firing until (a) you release the trigger or (b) you run out of ammunition. WW 2 fighter aircraft had fully automatic machine guns in the wings and, for bombers, in the turrets.
Right now there are some court controversies over definitions used by our U.S. Dept. of Alcohol, Tobacco, Firearms, and Explosives, or "ATF" as we usually call it. (The ATF didn't originally to cover all four of those types of things, but... the group has evolved.) Since full-automatic weapons ARE commonly prohibited, the exact definition of "fully automatic" has come under scrutiny. The crucial part of the definition is "number of rounds fired based on a single actuation of the trigger." If the answer is one, it is at most a semi-auto. If it is more than one, it is automatic, even it has a limiter to stop it at three or five rounds fired.
Hope that clarifies the matter. You can own non-auto and semi-auto firearms. Full-auto guns are restricted.
