The M1 Carbine is a small WWII rifle chambered for a more or less pistol-type .30 cal cartridge.
It was originally developed in the early 1940's as a "replacement" for the 1911 pistol for use by personnel not needing the M1 rifle.
It was to be issued to Artillery and support troops NOT normally engaged in combat, but who MIGHT be subject to a sudden enemy breakthrough.
Due to the needs of the military, the Carbine soon wound up being issued for front-line use.
The M14 is a 7.62/.308 rifle that was developed from the M1 rifle.
The M14 was developed in the late 1950's as an upgrade modification and replacement for the M1 rifle.
Unlike the Carbine, the M14 was a full Service or Battle rifle, like the M1, firing a cartridge that was basically a shortened 30-06 cartridge as used in the M1.
The M14 was capable of full-auto fire, but most were issued without the full-auto capability installed.
The M21 is a Sniper variation of the Service model of the M14.
It's basically just the M14 rifle, Match conditioned with tighter fitting parts and set up to use a telescopic sight.
The M21 was actually built by military armorers from standard M14 rifles, by fitting better quality, heavier barrels, altering the gas system for better accuracy, and by glass bedding the stock.
A special scope mount was installed, and the rifle was further "tuned" for better accuracy.
The same basic methods were used to build Match rifles for military target shooters for use in the National Match shooting course as done at Camp Perry, minus the telescope.
The civilian versions of the M14/M21 are built by a number of commercial makers.
These all use newly made, usually cast steel receivers, fitted with mostly used USGI M14 surplus parts.
These rifles have a variety of names, including the M1A as used by the commercial company known as Springfield Armory, which has NO relationship with the original US Springfield Arsenal at Springfield Mass.
These commercial rifles do not have the provision for full-auto fire and are NEVER the equal of the M14/M21 in quality.