screenshot (n.)

mid-14c., screne, "upright piece of furniture providing protection from heat of a fire, drafts, etc.," probably from a shortened (Anglo-French? compare Anglo-Latin screna) variant of Old North French escren, Old French escran "fire-screen, tester of a bed" (early 14c.). This is of uncertain origin, though probably from a Germanic source, perhaps from Middle Dutch scherm "screen, cover, shield," or Frankish *skrank "barrier," from Proto-Germanic *skirmjanan(source also of Old High German skirm, skerm "protection," Old Frisian skirma "protect, defend;" from PIE root *sker- (1) "to cut").

The sense of "anything interposed to conceal from view" is by c. 1600. The meaning "net-wire frame used in windows and doors" is recorded from 1859. Meaning "flat vertical surface for reception of projected images" is from 1810, originally in reference to magic lantern shows; later of movies. Transferred sense of "cinema world collectively" is attested from 1914; hence screen test "filmed test of performing abilities" (1918), etc.

The meaning "small fluorescent display on a TV set" is by 1946, extended to the display on a computer monitor by 1970, hence the monitor itself. The computer screen saver is attested by 1990. The meaning "window of an automobile" is by 1904. As a type of maneuver in sports, by 1934 (U.S. football, screen-pass). Screen printing recorded from 1918. Screen-door is from 1840. Screen-time "time spent watching a computer or television screen" is by 1999.

Middle English shot "a missile, arrow, dart" (senses now archaic or obsolete); "a swift movement, a gushing out," from Old English scot, sceot "a shot, a shooting, an act of shooting; that which is discharged in shooting, what is shot forth; darting, rapid motion."

This is from Proto-Germanic *skutan (source also of Old Norse skutr, Old Frisian skete, Middle Dutch scote, German Schuß "a shot"), from PIE root *skeud- "to shoot, chase, throw." The Old English noun is related to sceotan "to shoot." The meaning "discharge of a bow, missile," also is from related Old English gesceot.

The noun was extended to other projectiles (balls, bullets) by mid-15c. Especially "lead in small pellets, a small ball or pellet," a number of which are combined in one charge, which is attested by 1770 (shortened from earlier small shot, 1727).

The general sense of "an attempt to hit with a projectile" is by 1650s. Extended to sports (hockey, basketball, etc.) by 1772, originally in curling. It is attested by early 15c. as "range or distance of a missile in flight," hence "range" in general (c. 1600), as in earshot. 

Another original meaning, "payment" (perhaps literally "money thrown down") is preserved in scot-free; also see scot (n.). The notion of "throwing down" might have led to the meaning "a drink," first attested 1670s; the more precise meaning "small drink of straight liquor" is by 1928.

The sense of "hypodermic injection" is attested from 1904; the figurative phrase shot in the arm "stimulant" is by 1922. The broad meaning "a try, an attempt" is by 1756; the sense of "remark meant to wound" is by 1841. The meaning "an expert in shooting with a firearm" is from 1780; the sense of "a rocket flight" is by 1934. The camera-view sense is by 1958.

To call the shots "control events, make decisions" is American English, 1922, perhaps from sport shooting. Shot in the dark "uninformed guess, random attempt" is by 1885. Big shot "important person" is from 1861. 

By the rude bridge that arched the flood,

   Their flag to April’s breeze unfurled,

Here once the embattled farmers stood

   And fired the shot heard round the world.

[Emerson, from "Concord Hymn"]