Old English bor "instrument for making holes by boring or turning," from the source of bore (v.1). As "hole made by boring," early 14c. Meaning "cylindrical hole through a tube, gun, etc." is from 1570s; that of "interior diameter of a tube, caliber of a gun" (whether bored or not) is from 1580s. Hence figurative slang full bore (1936) "at maximum speed," from notion of unchoked carburetor on an engine.
"pierce or make a hole in with a drill or similar tool," c. 1600 (implied in drilling), from Dutch drillen "to bore (a hole), turn around, whirl," from Proto-Germanic *thr- (source also of Middle High German drillen "to turn, round off, bore," Old English þyrel "hole"), from PIE root *tere- (1) "to rub, turn," with derivatives referring to twisting, boring, and drilling. Related: Drilled, drilling. Compare thrill, the native English form of the word. Drill-press "drilling machine for boring holes in metal" is by 1850.
"tool for making holes in hard substances," 1610s, from Dutch dril, drille "a hole, instrument for boring holes," from drillen "to bore (a hole), turn around, whirl," from PIE root *tere- (1) "to rub, turn."