A magazine is an ammunition and explosives storehouse.
With respect to firearms, it is where the ammunition is stored, on board the firearm, for retrieval by the action of the firearm.
Not all firearms have magazines. A firearm without a magazine, or some other feeding device, is called a single shot.
Two barreled guns are called double barreled, or double barreled type (shotgun, rifle, etc.), or configuration (side by side, over/under), or simply a double.
Magazine fed guns are called repeaters.
Magazines can be fixed or detachable.
A fixed magazine is one not intended to be removed and replaced as a means of reloading. They are either an integral part of the firearm, as in a Model 1903 Springfield, or not readily removable, like the tubular magazines on many lever action rifles.
Magazines have a spring to move the rounds into position as they get used up. The spring pushes on the follower which follows the last round.
The cylinder on a revolver is kind of like a magazine, since it stores ammunition, but it is also not like a magazine, since it is more like a revolving chamber. Call it what you want. (But if you call it a magazine people will laugh and point.)
Many bolt action rifles have four or five round fixed magazines under the bolt. The rounds usually stack up in a zig zag fashion. Military bolt action rifles can often be reloaded with five round stripper clips.
Lever actions, pump actions, and lots of .22 rimfires often have tubular magazines. As the name implies tubular magazines are tubes, with a spring at one end to push the rounds down the tube where the action can get them. Tubular magazines are typically affixed under the barrel.
When used with centerfire cartridges, tubular magazines require flat topped bullets. This is because, to a centerfire primer, that pointy bullet it is sitting on looks an awful lot like a firing pin. Any kind of jarring, like recoil for instance, is likely to fire some, or all, of the cartridges in the tube. This is not a problem with flat topped bullets or rimfire priming.
Detachable magazines are most often box magazines. Other types include drum magazines, also called snail drums, rotary magazines which are like low capacity drum magazines, pan magazines as used on the Lewis Gun, and the unique 50 round polymer magazine of the FN P90.
If the capacity of a box magazine gets beyond about 20 rounds, they often have a forward curve. These are sometimes referred to as "banana clips" but a clip is intended to hold rounds together to make reloading magazines faster, whereas a magazine is intended to feed rounds directly to the action of the firearm.
Detachable box magazines are usually single stack or double stack. In a single stack magazine the rounds sit directly on top of one another. This keeps the magazine narrower.
In a double stack magazine the rounds zig zag back and forth. This allows more ammo in the same length, but is wider.
Some double stack magazines are set up to strip rounds alternately from the left and right, like the AR15 magazine pictured, while others force the top round to a central position.
Clips hold ammunition together for fast loading of magazines. Magazines feed ammunition to the action of the firearm.
Stripper clips hold a number of rounds of ammunition together in a way that makes it easy to reload a fixed or box magazine. The US government packaged a gazillion (an industry term) rounds of .30-'06 ammo on five round stripper clips during WWI and WWII. The full stripper clip is inserted in the stripper clip guide of the rifle and the rounds are pushed down with a thumb into the magazine.
The M1 Garand of WWII uses an en-bloc clip. This clip holds eight rounds of .30-'06 and is inserted in the rifle along with the ammo. In operation, the follower lifts the ammo, but not the clip, as rounds are fired. After the last round is fired the clip ejects making a distinctive ping sound.
Moon clips hold ammo for revolvers. They come in full moon, half moon, and two round versions. The cylinder of your revolver must be designed or modified to use moon clips. With practice moon clips allow very fast reloads.
Speed loaders also hold revolver ammunition. They must be matched to the chambering, make and model of your revolver. Insert the cartridges and twist the knob to release them for fast reloads.
Speed Strips are flexible rubber gizmos. Put a cartridge in each hole and it keeps them together and in the same orientation. To use them you stick the cartridges in the revolver cylinder a couple at a time and then peel off the rubber speed strip.