What are the differences between Jesuits, Franciscians, Dominicians, etc? How many different types/branches/
are there?
I guess a chart listing them all out and the different characteristics would be really benefical here.
Thanks for answering my question!!! 
Well, there are Diocesans and Religious. Those who mentioned would fall under religious. That means they belong to a Religious Order and would have vows, which includes poverty. Diocesan priests do not have vows, they earn a salary and own their own property. I think religious priests would also get a salary if they do work for a diocese, but all that money goes directly to their Order, and not a penny is left in their pockets.
Each âorderâ has a particular charism that they follow that is detailed in their respective rule or constitution.
Hopefully Br. JR, a Franciscan and Br. David, a Carmelite, will chime in on this thread and give the perspectives of their particular families.
I can tell you a little about the Jesuits or Society of Jesus.
They were founded by St. Ignatius of Loyola, who was quite the character before he had his conversion experience.
Jesuits make the traditonal vows of poverty, celebacy & obedience. They also make a special vow to do basically whatever the Pope asks of them.
In their beginning, many Jesuits were responsible for bringing Christianity to the âNew Worldâ of the 16th century.
*The Spiritual Exercises of St. Ignatius *and the *Constitution of the Society of Jesus *are the foundation of the Jesuit charism, which in a nutshell is to "find God in all things"
The Jesuits are also the only order, I believe, that are not bound to recite the Divine Office.
The reason being that Ignatius felt it more important to balance contemplation with work, so that everything he did was prayer.
As the Jesuit motto says-
Ad Majorem Dei Gloriam- all for the greater glory of God!
The Jesuits were also formed to fight off Protestantism during the Reformation. They were also considered a large aspect of the Counter-Reformation. Iâve als heard that St. Ignatius was VERY anti-Protestant.
OscarsMama, there are five broad categories which we can say priests fall into:
We may split up the most famous orders of the Church by this template.
Archdiocese of Halifax, Diocese of Birmingham⌠etc. 
The Order of Friars Minor, the Order of Friars Preachers, Order of the Brothers of Our Lady of Mount Carmel, Servites, Minims, Trinitarians, etc.
Order of St. Benedict, Order of Cistercians, Trappists, etc.
Society of Jesus, Oratory of St. Philip Neri, Piarists, etc.
Augustinian canons, Praemonstratensians, etc.
Diocesan priests are your average âsecular priestâ. They celebrate the holy Mass, preside over funerals, arrange the affairs of their parish, and generally distribute sacramental grace. They do not necessarily live in community, though a rectory often houses more than one diocesan priest. Their vow is one of obedience to their bishop.
Mendicants/friars live in community by necessity, and do not necessarily celebrate the holy Mass or the sacraments. The Friars Minor style themselves primarily a brotherly order that happens to have priests for sacramental necessities. The Friars Preachers style themselves primarily a priestly order that happens to have brothers for support. These men are not necessarily attached to one house or community, and can be moved or sent across the world. Different friars pray their Divine Office/Liturgy of the Hours differently. These all take the vow of poverty, chastity, and obedience to their superiors.
Monks live in community by necessity, and do not necessarily celebrate the holy Mass or the sacraments. They exist primarily to contemplate God in prayer, isolation from the world, and in self-sufficiency through hard work. These men are necessarily attached to one house/cloister, and vow to be stable in remaining at this one house for the duration of their lives. They pray the Divine Office/Liturgy of the Hours in full choir with all monks (priests and lay) participating. These do not generally go âout into the worldâ as the friars do.
Clerks/clerics regular are essentially diocesan priests who can be sent anywhere in the world by their superior. They are bound to say the Divine Office like any other priest, but they have specific beliefs very unique to them. Jesuits are absolutely different from Oratorians, though both are clerks regular. These men are necessarily priests, though there are many Jesuit âbrothersâ who support the priests. Clerks/clerics are generally created as Societies of Apostolic Life for the express purpose of ordination to the clerical state.
Canons regular are the rarest these days, and theyâre my favourite. They are essentially a cross between the diocesan priest and the monk. They take a vow of obedience to their superior, and of stability/loyalty to their particular house, but this is often the local cathedral. They are free to move around in their diocese, unlike monks, but they also say their Divine Office in community, in choir, unlike clerks/clerics regular, and unlike diocesan priests. Theyâre a very interesting mix of public prayer, diocesan sacramental duty, saying Mass, living in cloister, and moving among the laity.
I just love the variety and diversity of the Church!
Donât forget the religious congregations!
By the Law all of the religious orders are considered Religious congregation
vatican.va/roman_curia/congregations/ccscrlife/documents/rc_con_ccscrlife_profile_en.html
As for the scheme historically the sequence (as they appaered) is:
diocese, canons (from the hermits), monks (Benedictines etc), friars (Franciscans, Domicans), clerical orders (Jesuits etc).
Recently there are new forms like the Opus Dei, priestly fraternities (FSSP)
All of the categories except the monks get their jurisdiction (to celebrate licit masses, hear confessions and witnessing marriages) from the territorial Ordinary (I am not sure about the Opus Dei)
I always thought friars were always priests and monks were always brothers. There is a Franciscan (Conventual) parish about 10 mile from my family and I thought the ordained were called friars and the brothers were called monks.
I learn something new everyday. 
I also love the diversity. I love comparing and contrasting the different forms of culture in the Church and its history.
ajpirc, it can get very confusing, but I can at least give an idea from my âspiritualâ Order, the Dominicans. There are three levels to this family of St. Dominic:
Not every Dominican in history was ordained a priest, though their Order is more priest-oriented than the Franciscans. Most Dominican saints were ordained, such as Albertus Magnus, Thomas Aquinas, and the Holy Father of the Order himself. Naturally the sisters are never ordained, and next to them you have the brothers (called âco-operator brothersâ today) such as St. Martin de Porres. The laity take part in the charism of the Order by receiving a small habitual scapular, and go into formation to preach and live in the mode of sainthood. The Order is united more by preaching and theological inquiry than by rank, status, or intimate familial, poor, Franciscan-like bonds.
A âbrotherâ may be a monk, friar, or cleric regular. Different sorts of brothers do different things. I donât know if Canons have a brother-rank.
Some Franciscans (the Capuchins especially I believe) also call themselves monks, just to add to the confusion I guess
The basic divisions already given are pretty good though, just the language people actually use doesnât always line up exactly to such orderly categories.
I personally like to deal in dichotomies, so I more often think of the division into either secular vs. religious priests or active vs. contemplative (not the same division, as most religious priests are also in more or less active vocations). Just another, more simplistic way of viewing it all.