"government-sanctioned freebooter of the seas," 1540s, from French corsaire (15c.), from Provençal cursar, Italian corsaro, from Medieval Latin cursarius "pirate," from Latin cursus "course, a running," from currere "to run" (from PIE root *kers- "to run"). The sense of the Medieval Latin verb evolved from "course" to "journey" to "expedition" to an expedition specifically for plunder. As "a privateering pirate ship" from 1630s.
The name in the languages of the Mediterranean for a privateer; chiefly applied to the cruisers of Barbary, to whose attacks the ships and coasts of the Christian countries were incessantly exposed. In English often treated as identical with pirate, though the Saracen and Turkish corsairs were authorized and recognized by their own government as part of its settled policy towards Christianity. [OED]