First let us review. First you have the diocesan hierarchy; bishop, priest, deacon, laity. You have the diocesan hierarchy of the diocese of Rome; popes, cardinals and so forth, but still essentially bishop, priest, deacon. Then you have the monastic orders. Men and/or women who live in cloisters and take solemn vows.
Now, we need to explain canons and canons regular. Canons are priests or clergy who live a communal life in order make sure the liturgy of the hours (also called the breviary or the divine office) is prayed properly. They form a sort of middle ground between the cloistered monastic orders and the diocesan or secular clergy (secular here means living in the present age ”saeculum” in Latin) they don’t take solemn vows or live in a cloister. They exercise their ministry in the wider church but live communally. Some follow the rule of life that is almost monastic proposed by St. Augustine in the fourth century, which includes poverty. These are called Canons Regular. Regular comes form the Latin word “regulum’ or “rule.” They live by a rule of life, hence they are regular or regulated. It does not imply that they are “regular” or “normal.” Heaven forfend. They became popular in the 700's and have been around since.
The next group to deal with are the mendicant orders. These are orders who live by the charity of others and usually preach and teach such as the Franciscans, Dominicans, Servites, Carmelites and Augustinians, all founded in the 1200's at a time when the Church was struggling with its identity as a religious/political body. They were founded with an eye to restoring the Church to holiness by the witness of a holy and simple life. They are not usually priests, though some of their number are ordained as needed for the life and the work of the order. We diocesan priests don’t have much time for actual holiness because we have to make sure the hall is locked and that there is toilet paper in the ladies’ room. They take vows of poverty and the men in the orders are called friars, derived from the Latin word “frater” or “brother.” Women mendicants are usually called sister.
Add to these, the religious congregations which are communities of men or women who live according to a rule of life, take simple vows and are pretty much indistinguishable from the mendicant orders. The important thing about them is that they are oriented around a particular work, such as teaching, or hospital work or the missions. To these, add the third orders, which are usually lay men and women who are trying to live holy lives by association with the spirituality and rule of one of the religious orders.
So there you have it. Monastic orders that live cloistered lives of prayer and work and the Religious Orders. Count with these the mendicant order and religious congregations that live a more public life in a specific work for the good of the church.
The Jesuits! You didn’t mention the Jesuits!
I’m getting to that. The Jesuits, more precisely the Society of Jesus, are a religious order of priests and brothers who work in education and missionary evangelism. They were founded by St. Ignatius of Loyola in 1534. St Ignatius was wounded in the battle of Pamplona in Spain and, while convalescing, he experienced a religious conversion. Ignatius gathered six young men with whom he vowed poverty, chastity, and obedience to the pope. They arrived at a pivotal moment in Christian history when much of the Catholic world had broken apart after Luther’s revolt. The Jesuits won much of Europe back to Catholic Christianity by their dedication to education, holiness of life and the obedience to the papacy.
So that’s it! 1)The diocesan structure of Bishop, Priest and Deacon 2) the Cloistered Monks and Nuns and 3) the Religious Congregations of Brothers (also called Friars) and Sisters. All the different flavors of Monks, Nuns, Friars, Sisters, Bishops, Popes, Priests, Deacons, Third Order Members, protonotaries apostolic, monsignors and Associations of the Faithful fit into one of these three categories. Simple, in a complicated sort of way.
Rev. Know-it-all
PS There is no truth to the irreverent old joke “How many Jesuits does it take to screw in a light bulb?” Answer: “It takes two. One to call the electrician and one to make the martinis.” This is patently false. It depends entirely on the quantity of martinis to be made.