late 15c., "a guide," from Anglo-French directour, French directeur, agent noun from Latin dirigere "set straight, arrange; give a particular direction to," from dis- "apart" (see dis-) + regere "to direct, to guide, keep straight" (from PIE root *reg- "move in a straight line").
Corporate sense of "one of a number of persons having authority to manage the affairs of a company" is from 1630s; theatrical sense of "the leader of a company of performers" is from 1911.
1630s, "of or befitting to a master or teacher or one qualified to speak with authority," from Medieval Latin magisterialis "of or pertaining to the office of magistrate, director, or teacher," from Late Latin magisterius "having authority of a magistrate," from magister "chief, director" (see master (n.)).
By 17c. often with a suggestion of "arrogant, imperious, domineering." Meaning "holding the office of a magistrate, proper to a magistrate" is from 1650s (see magistrate). Related: Magisterially.
"master of music, great teacher or composer," 1797, from Italian maestro, literally "master," from Latin magistrum, accusative of magister "chief, head, director, teacher," contrastive adjective ("he who is greater") from magis (adv.) "more," from PIE *mag-yos-, comparative of root *meg- "great." Applied in Italian to eminent musical composers. Meaning "conductor, musical director" is short for maestro di cappella (1724), literally "master of the chapel" (compare German kapellmeister).
1570s, "forming part of the accepted course of teaching," a sense now obsolete, from Latin magistralis "of a master," from magister "chief, director" (see master (n.)). Meaning "authoritative; of, pertaining to, or befitting a master" is from c. 1600. In pharmacy, of a remedy, etc., "devised by a physician for a particular case, prepared for the occasion" (c. 1600).