What the word does now
In present-day English, shot is the firing of a weapon, the pellet or ball that leaves it, and the attempt to hit. The same noun covers a try at almost anything, a take with a camera, a small measure of spirits, and a hypodermic injection. As an adjective it can mean exhausted or worn out, because it is also the past form of shoot. Those later uses sit a long way from a bowstring, yet they grew from one native stock rather than from a later loan.
A Germanic noun already in Old English
The origin of the word shot is not a medieval import. Speakers had the noun before 1150. Old English wrote it as scot and sceot, with a related form gescot or gesceot. The early senses were an act of shooting, whatever was sent forth, and swift or darting motion. Middle English kept the word as shot, schot, and several regional spellings. Historical dictionaries treat it as inherited from Germanic, with first use in the Old English period, and they take the Middle English noun from those Old English forms.
The noun stood beside the verb sceotan, to shoot. That pairing is still the shape of the modern pair: shoot for the action, shot for the result, the missile, and the past tense. The word is not a prefix glued onto a foreign root inside Modern English. It is the old noun of the act, kept through the sound changes that turned sc into sh.
The older root, and the family around it
Comparative reconstruction gives a Proto-Germanic neuter noun, written by some scholars as skutą, related to the verb meaning to shoot. Sister forms across the family make the picture clearer than any single English spelling. German has Schuss for a shot and Geschoss for a projectile. Dutch has schot. Swedish has skott, Danish skud, Icelandic skot. West Frisian keeps skot. Old Norse had skot and a related skutr. These are cognates, not later copies of the English word.
Behind the Germanic layer, dictionaries reconstruct a Proto-Indo-European root meaning to shoot, chase, or throw. One common spelling of that root is skeud-; another is (s)kewd-. The difference is mainly how the reconstruction is written, not a quarrel about the English history. Suggested relatives outside Germanic include a Sanskrit verb for hastening, Lithuanian skudrus for something quick or nimble, and an Old Church Slavonic verb for throwing out. Those links are comparative guesses, not quotations from a speaker of the parent language, and they should be held lightly.
English also keeps other members of the same stock: shoot itself, and, by more winding routes, shut, shuttle, and sheet in both the cloth and the sail-rope senses. The useful morphological fact is simple. Shot names the sending and the thing sent. It is not a folk-etymology blend and not a clipping of a longer learned word.
How the senses moved
The oldest English uses pointed to missiles such as arrows and darts, and to the motion of sending them. Those senses later faded or became technical. By the middle of the fifteenth century the noun had spread to other projectiles, including balls and, later, bullets. Small lead pellets, the load of a shotgun, are recorded in the eighteenth century, shortened from the earlier phrase small shot.
Range followed the flight. Early fifteenth-century English already used the word for how far a missile would travel. From that spatial sense came a wider idea of range, still audible in earshot, the distance within which a sound can be heard.
Once the noun named an attempt to hit, it was ready to leave weapons. Trying to strike with a projectile is dated to the seventeenth century. Sports uses appear by the late eighteenth century, first in curling, then in the ball and puck games that borrowed the same picture. A try at anything, not only a target, is recorded by the mid-eighteenth century. A cutting remark, meant to wound, belongs to the nineteenth. A person judged by skill with a firearm is a shot from the late eighteenth century. A rocket flight is a twentieth-century extension. A camera take is later still, from the 1950s.
Medicine and drink arrived as a single measured discharge. A hypodermic injection is attested from the first years of the twentieth century; the figurative stimulant, a shot in the arm, follows soon after. A drink appears from the 1670s; the narrower bar sense of a small measure of straight liquor is twentieth-century. Whether that drinking sense comes from tossing liquid back, or from throwing down money for a share, is not settled. The payment idea is a plausible bridge, not a proven one.
American slang of the early twentieth century made the past participle mean ruined or used up. That is the same form as wounded by a bullet, recorded in the nineteenth century, stretched to people and machines that no longer work. To call the shots, to control what happens, is American English from the 1920s, perhaps from sport shooting, though that link is offered with caution. A shot in the dark, an uninformed guess, is nineteenth-century. Big shot, an important person, is a little older.
Payment, and a quiet doublet
Old English scot also named a contribution or tax. That payment sense survives most clearly in scot-free, originally free of a required share, later free of penalty. French écot, a share, and related Romance forms come from the same Germanic stock, not the other way around. English scot is treated as a doublet of shot: two words from one older noun, split by spelling and by sense. In some speech a person’s shot is still the round they pay for.
The two histories are easy to mix because the spellings met in the middle. One line is the missile and the act of shooting. The other is a share thrown into a common reckoning. Both sit on Germanic verbs of sending or putting down. German and Dutch show similar old splits between shooting and other senses. English did not need a Norman label to make the word common. It was already in the language, then widened as guns, sport, cameras, and clinics gave it new work.
The concrete remainder is this: shot is not a modern coinage for firearms. It is an Old English noun for sending something forth, still doing that job after the missile changed from dart to bullet, and after the target became a hoop, a lens, a vein, or a glass.