Religious is a term with both a technical definition and folk use.
Technical definition
One whom practices any religion. In the lexicon of the Church, especially the Roman Catholic, Anglican, and Orthodox, religious as a noun usually refers to a member of a religious order of monks, nuns, friars, clerics regular, or other individuals who take the three vows of poverty, chastity, and obedience (the evangelical counsels). Neither of those groups should be identified as clergy, which in Catholicism includes bishops, priests and deacons.
Though seemingly redundant, there are also "religious priests" used in reference to priests who are members of orders, such as the Society of Jesus or the Franciscans. Such clergy are differentiated from diocesan priests who serve under a bishop or archbishop who has jurisdiction over a geographically defined diocese. Monks and Nuns are part of the religious ministry.