Let’s start from scratch. There are only three Sacred Orders of clergy: 1) Bishops; 2) Priests; 3) Deacons.
Bishops are “overseers” and usually manage groups of parishes called a “Diocese.” A bishop has almost complete authority in his own diocese, as long as he doesn’t violate the Law or Faith of the Church (more on that later). Bishops exercise pastoral care over everyone in their diocese, in all aspects of the life of the Church. It is the bishop’s job to make sure Mass is available, Confessions are heard, and that the rules of the Church are followed. To be able to do this, a bishop can celebrate all Seven Sacraments.
However, a bishop can’t do all of this on his own, so he is assisted by Priests. Priest can celebrate most of the Sacraments, but they only celebrate any Sacrament with their bishop’s permission (and cannot ordain people at all). Most priests are pastors: they are responsible for the spiritual care of people living in a certain area, or belonging to a certain group. The bishop assigns this priest to say Mass, and minister to the people who go to his church. A priest leads this people, and helps them grow spiritually.
Priests are sometimes assisted by deacons, who help at Mass, and with the care of people in the parish.
Most priests and deacons work in parishes, but some help the bishop in different ways by teaching, managing offices for the diocese, or ministering to special places (nursing homes, prisons, hospitals, schools, et c.).
These are the three major divisions in clergy.
However, some bishops are given special honors. A bishop of a very large and important diocese (called an archdiocese) is given the title “archbishop.” A small group of bishops are chosen to become Cardinals, who advise the government of the Church as a whole, and elect the Pope. The Pope is a bishop who manages the Law of the Church, and exercises pastoral responsibility over all Christians. It’s important to recognize that the pope’s job isn’t to change the law, but to preserve it. This is why a pope cannot change Church teachings on subjects like abortion, homosexual marriage, and ordaining women.
While archbishops, cardinals, and popes may have special titles and responsibilities, they are still only bishops, someone is not ordained a pope, cardinal, or archbishop.
Likewise, some priests are honored with the title “Monsignor,” but they are not anything more than a regular priest: they are just recognized in a special way for their service.
Many priests, deacons, and bishops work together in a conglomerate of offices called the Roman Curia, which manage the Church as a whole. If the bishop has a question, or need help, he will go to the Curia, and the Curia will involve themselves if there is trouble with a bishop or priest.
There is another division of clergy that is separate from everything we’ve talked about so far. This is the division between secular and religious clergy.
Secular clergy are the priests you would often see at a church, and they are bound to serve a bishop, and serve that bishop and his successors for the entirety of their priesthood. These priests do not take a vow of poverty, but live simply, and are chaste celibates in the Western Church.
Religious clergy are men who belong to an Order, and are ordained to provide the Sacraments for the other people in that order.
Women Religious (that is, nuns and sisters) cannot be clergy, because women cannot be ordained. Usually, a priest-chaplain is assigned to provide the Sacraments for these women.
Different orders might have different jobs they work in. Common ones are teaching, working with the poor, running missions, or just praying for the world as a whole.
Please let me know if I missed anything or made any mistakes. I tried to make this as simple as possible, so I purposely didn’t touch on everything, but I tried to make this a good overview.
