The Catholic clergy is organized in a strict, sometimes overlapping hierarchy:
Pope: Head of the church, he is based at the Vatican. The pope is infallible in defining matters of faith and morals.
Cardinal: Appointed by the pope, 178 cardinals worldwide, including 13 in the U.S., make up the College of Cardinals. As a body, it advises the pope and, on his death, elects a new pope.
Archbishop: An archbishop is a bishop of a main or metropolitan diocese, also called an archdiocese. A cardinal can concurrently hold the title. The U.S. has 45 archbishops.
Bishop: A bishop, like a priest, is ordained to this station. He is a teacher of church doctrine, a priest of sacred worship, and a minister of church government. The U.S. has 290 active bishops, 194 head dioceses.
Priest: An ordained minister who can administer most of the sacraments, including the Eucharist, baptism, and marriage. He can be with a particular religious order or committed to serving a congregation.
Deacon: A transitional deacon is a seminarian studying for the priesthood. A permanent deacon can be married and assists a priest by performing some of the sacraments.
Edit: I used to know all that off the top of my head, but I have lapsed for many years. The orders it mentions for the Priests would be Jesuits, Franciscans, Dominicans, Benedictines, etc. https://en.wikipedia.org/wiki/Catholic_religious_order