Etymology
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spigot (n.)
late 14c., "plug used to stop the hole of a cask," according to Barnhart probably from Old French *espigot (compare Gascony dialect espigot "core of a fruit, small ear of grain"), diminutive of Old Provençal espiga "ear of grain," from Latin spica "ear of grain" (see spike (n.2)). Meaning "valve for controlling the flow of a liquid" is from 1520s; the connecting notion is "that which controls or restrains."
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tap (n.1)
"stopper, faucet through which liquid can be drawn," Old English tæppa "tap, spigot," from Proto-Germanic *tappon (source also of Middle Dutch tappe, Dutch tap, Old High German zapfo, German Zapfe). Originally a tapering cylindrical peg for a cask, then a hollowed one to draw from it (compare sense evolution of spigot). Phrase on tap "ready for use, ready to be drawn and served" is recorded from late 15c. Tap-wrench, used in turning one, attested from 1815.
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faucet (n.)
c. 1400, from Old French fausset (14c.) "breach, spigot, stopper, peg (of a barrel)," which is of unknown origin; perhaps diminutive of Latin faux, fauces "upper part of the throat, pharynx, gullet." Not in Watkins, but Barnhart, Gamillscheg, and others suggest the Old French word is from fausser "to damage, break into," from Late Latin falsare (see false).

Spigot and faucet was the name of an old type of tap for a barrel or cask, consisting of a hollow, tapering tube, which was driven at the narrow end into a barrel, and a screw into the tube which regulated the flow of the liquid. Properly, it seems, the spigot was the tube, the faucet the screw, but the senses have merged or reversed over time. OED reports that faucet is now the common word in American English for the whole apparatus.
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pin (n.)

late Old English pinn "peg or bolt of wood or metal used to hold things in place or fasten them together," from Proto-Germanic *penn- "jutting point or peak" (source also of Old Saxon pin "peg," Old Norse pinni "peg, tack," Middle Dutch pin "pin, peg," Old High German pfinn, German Pinne "pin, tack") from Latin pinna "a feather, plume;" in plural "a wing;" also "fin, scoop of a water wheel;" also "a pinnacle; a promontory, cape; battlement" (as in Luke iv.9 in Vulgate) and so applied to "points" of various sorts, from PIE root *pet- "to rush, to fly."

De Vaan and Watkins say Latin pinna is a derivative of penna, literally "feather" (see pen (n.1)); older theories regarded pinna as a separate word from a root meaning "sharp point." The Latin word also was borrowed in Celtic: Irish pinne "a pin, peg, spigot;" Welsh pin "a pin, pen."

The transition from 'feather' to 'pin' (a slender or pointed instrument) appears to have been through 'pen,' a quill, to ' pen,' a style or stylus, hence any slender or pointed instrument [Century Dictionary]

As a part of a lock or latch, c. 1200; as a control for a mechanical device, late 14c. The modern slender wire pin, used as a fastener for clothing or in sewing, is attested by this name by late 14c., perhaps late 13c. Transferred sense of "leg" is recorded from 1520s and holds the older sense. The meaning "wooden stick or club set up to be knocked down in a game" (skittles, bowling, etc.) is by 1570s.

Pin-money "annual sum allotted to a woman for personal expenses on dress, etc." is attested from 1620s. Pins and needles "tingling sensation" is from 1810. The sound of a pin dropping as a type of something all but silent is from 1775.

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