"small hanging piece from a garment," c.1400, perhaps from a Scandinavian source (cf. Norwegian tagg "point, prong, barb," Swedish tagg "prickle, thorn," Middle Low German tagge "branch, twig, spike"); cognate with tack (n.1). Meaning "label" is first recorded 1835; sense of "automobile license plate" is recorded from 1935, originally underworld slang. Meaning "an epithet, popular designation" is recorded from 1961, hence slang verb meaning "to write graffiti in public places" (1990).
"children's game," 1738, perhaps a variation of Scot. tig "touch, tap" (1721), probably an alteration of Middle English tek "touch, tap" (see tick (2)).