Is there a difference between an m14 and m1 carbine?

Yes, quite a few, the M-14 is a full size battle rifle (later a marksman's rifle), and fires a full size rifle cartridge (7.62x51mm NATO), while the M-1 Carbine is intended as a small personal defence weapon at close to medium ranges, and it fires a .30 cal. Carbine cartridge, which is comparible in size and effectiveness to a .357 magnum, ideal for what the Carbine was designed for. The M-14 was also originally designed to be loaded by two stripper clips (ten rounds per clip) through the top of the receiver, fed into the box magazine, the carbine, was loaded by removing the magazine, then reloading a new one. Later, the M-14's loading procedure was changed, and troops were taught to reload the box magazine and replace it with new ones, like most modern rifles were at that time, instead of using the slow, two stripper clips feed. The M-1 Carbine was initially also only a semi-automatic design, while the M-14 was always able to fire in semi or full automatic.