early 13c., in frere menour "Franciscan friar," literally "minor friar," from Latin minor "less, lesser, smaller, junior," figuratively "inferior, less important," which was formed as a masculine/feminine form of minus on the mistaken assumption that minus was a neuter comparative, from PIE root *mei- (2) "small." Compare minor (n.). In some cases the English word is from Old French menor "less, smaller, lower; underage, younger," from Latin minor.
Meaning "underage" is from 1570s. Meaning "lesser or smaller (than the other)" in English is from early 15c.; that of "comparatively less important" is from 1620s. The musical sense is from 1690s in reference to intervals (and to tonalities and scales characterized by a minor third), so called because the interval is lesser or shorter than the corresponding major interval. Of triads or chords by 1797; their emotional effect is notable mournful, mysterious, gloomy, or wistful, hence figurative and extended senses. In the baseball sense, minor league, made up of teams below the major league, is from 1884; the figurative extension of that is recorded by 1926.
c. 1300, "man consecrated to service in the Christian Church, an ecclesiastic;" also "an agent acting for a superior, one who acts upon the authority of another," from Old French menistre "servant, valet, member of a household staff, administrator, musician, minstrel" (12c.) and directly from Latin minister (genitive ministri) "inferior, servant, priest's assistant" (in Medieval Latin, "priest"), from minus, minor "less," hence "subordinate" (from PIE root *mei- (2) "small") + comparative suffix *-teros. Formed on the model of magister (see master (n.)).
Minister views a man as serving a church; pastor views him as caring for a church as a shepherd cares for sheep; clergyman views him as belonging to a certain class; divine is properly one learned in theology, a theologian; parson, formerly a respectful designation, is now little better than a jocular name for a clergyman; priest regards a man as appointed to offer sacrifice. [Century Dictionary, 1895]
The political sense of "high officer of the state, person appointed by a sovereign or chief magistrate of a country as the responsible head of a department of the government" is attested from 1620s, from notion of "one who renders official service service to the crown." From 1709 as "a diplomatic representative of a country abroad." A minister without portfolio (1841, in a French context) has cabinet status but is not in charge of a specific department.