The story goes that a monastery in England decided to open up a roadside fish-and-chips stand to help support themselves. One wag who approached the stand quipped to the religious manning it, "Are you the fish friar?"
"No," the brother replied straight-faced, "I'm the chip monk."
Okay, so the joke's not that funny. But it does bring forth a distinction that you may not be aware of if you're not Catholic … and, given recent history in religious formation, perhaps even if you are Catholic.
"Monk" stems from the Greek word monachōs, and is a generic word for anyone who lives a life separated from others and devoted to prayer or meditation, whether Christian or not. In the Western Christian tradition, while the monastic orders are also called "eremitical" (from Gr. erēmitēs through L. ĕrēmīta, = "of the desert"), the term "hermit" is usually restricted to a person who lives completely separated from everyone else, while a monk lives with other monks. The Carthusians (Order of St. Bruno) straddle this distinction by a rigid limitation of the contact its members have even with each other; most other orders live their daily cycle of work, prayer and study in community, guided by their adaptation or interpretation of the Rule of St. Benedict of Nursia.
"Friar" stems from the Latin frater through the French frère (= "brother"). In general, friars belong to a mendicant order. Historically, the eremitical orders supported themselves with farming, livestock-raising and other forms of manual labor, which entailed the communal possession of land and buildings. By contrast, the mendicant orders owned little beyond their residences and the bare minimum of possessions necessary to carry out their missions, subsiding on contributions from the community. Nowadays, both types of orders may run hospitals, outreach centers, schools and other public services, so this distinction between the two isn't always clear in practice.
Both monks and friars live in community and chant the Divine Office in choir; they both take the traditional solemn vows of poverty, chastity and obedience. Some orders may take an additional vow according to their missions. But while a life of prayer and contemplation is the monk's raison d'être, the friar lives to serve the larger community through charitable works. Moreover, while most monks are tied to a specific monastery for life, friars may be transferred from one convent to another according to the needs of the order. In the case of both, while some monks and friars are ordained, their primary function is prayer and celebration of the liturgy, not administration of the sacraments. For this reason, not all monks and friars are called to Holy Orders.
Besides monks and friars, there are also orders of priests and deacons who profess the evangelical vows. Canons regular, similar to monks, are usually attached to a specific church, most often a cathedral, while clerks regular, like friars, may be moved according to the needs of the order. They're called "regular" (from the Latin regula, = "rule") because as part of their communal life they have adopted a constitution, often the Rule of St. Augustine; the most notable order of clerks regular, the Society of Jesus ("Jesuits"), follow a rule drawn up by St. Ignatius Loyola. Unlike the monastic and mendicant orders, though, the focus of these clerical orders is on the sacraments and the sacred mysteries, rather than on prayer and contemplation; while ordination is occasional and incidental to monks and friars, it's essential to canons and clerks.
Just as many people use "monk" and "friar" interchangeably, so do they use the words "nun" and "sister". All nuns are religious sisters, but not all religious sisters are nuns. Nuns, like monks, live in communities, take solemn vows and chant the Divine Office in chorus. (However, since women can't aspire to Holy Orders, nuns must either have at least one priest attached to their monastery, or—if their community is too small to support a priest—have recourse to a parish church.) Like monks, nuns are tied to a specific monastery or abbey, and are cloistered to various degrees. Religious sisters who aren't nuns generally profess simple vows of chastity and obedience; while they don't renounce personal property, their use is at the discretion of their communities, especially their superiors. Sisters of mendicant orders, like friars, direct their work to public service.
(What's the difference between a simple vow and a solemn vow? Not much, anymore. Under the 1917 Code of Canon Law, a solemn vow of chastity invalidated all attempts at marriage, while a simple vow merely made a marriage wrongful but still binding. Under the 1983 Code, the important distinction is now between temporary vows, from which one can be released by the appropriate superior or hierarch, and perpetual vows, from which can only be released by the Pope; calling one set "solemn" and another "simple" is retained as a tradition but holds no legal ramifications.)
There are also "third" orders of lay men and women who act in an auxiliary role with the "first order" of monks and friars and the "second order" of nuns. These tertiary orders originally developed in response to the desires of people who aspired to the spirituality of the traditional first and second orders but who could not fully adopt the monastic or conventual life (often because they were married, or had familial or legal responsibilities). Third orders are considered "regular" if the members profess the evangelical vows; "secular" orders may only require temporary vows, or solemn and public promises. Also, while third orders regular usually live in community under a common rule, the third order seculars usually don't.
Forming—erecting—a religious order isn't quite as simple as getting a few men or women together to make a couple of promises and share a house. Rather, the whole process may take some years, and is guided by the local bishop under Part III, Section I of the Code of Canon Law in consultation with the Holy See.
First, the bishop may require an intermediate step to test their vocations, such as serving a novitiate at a nearby monastery or convent. Second, the group must draw up a constitution or charter which will spell out not only the rules governing the order but also its mission, as well as its spirituality. Third, since part of the monastic life is daily participation in Mass, the bishop may also require some of the (male) members to study for ordination to the priesthood or for the group to have access to a parish church; at its founding, the order must have a residence with an oratory for the Liturgy of the Hours and adoration of the Eucharist. Between the day the prospective founder(s) approach the bishop and the day the bishop issues his decree formally erecting the order many thing can intervene to delay or even foil the foundation.
I should also note, in fairness, that while the vast majority of Christian monastic orders in the world are Catholic or Orthodox, the Anglicans and Lutherans also have orders of monks and nuns.
It's also worth noting that, while the religious orders suffered a tremendous loss of membership in the social upheaval of the 1960s and '70s, there are signs that they're coming back to life. Many observers believe that the uptick in aspirants to the religious life is both in reaction to liberal Christian attempts to "baptize" secular ideology and in response to a perceived loss of Catholic identity and spirituality, the latter probably due to the former. Others believe that, just as there's a movement within the Church driving a "reform of the (Vatican II) reform", there's also a movement growing among young people that's driving a "rebellion against the rebellion", especially as a newly aggressive and empowered secularism forces otherwise indifferent Christians—especially Catholics—to choose sides in the culture wars. In this respect, members of religious orders appear to more young people to combine the best of both worlds: outsiders to society at large, yet fulfilling socially respectable roles; distinctive for their dress, separate from the community, yet filled with happiness and peace.
If Western civilization is headed for a new "dark age", as I wrote before, I fully expect Christian monasteries to save it, like they did after the collapse of the Roman Empire.
 The Eastern Orthodox monastic tradition has some salient differences which I won't treat here.
 Formally known as "Liturgy of the Hours". A collection of prayers and readings from the Bible, the Church Fathers and various saints, spoken at set times throughout the day, and rotated in cycles according to the liturgical calendar.
 While normal English usage uses "convent" almost exclusively for the residences of women religious, technically members of mendicant orders live in convents, while monastic communities live in monasteries, abbeys or priors.
 Saint Benedict's Rule, one of the most influential works in European history, has been either adapted or adopted by most religious orders over the last 1,500 years; while easy to modify for specific missions and environments, it doesn't ask for improvement.
 Here, "spirituality" means the particular forms of prayer, meditation and adoration the order will incorporate into its spiritual life, and how they will be regulated.
 The theology and spirituality of these Protestant monastics are very close to traditional Catholicism, which may be part of their appeal, since both denominations have clusters of members who believe Henry VIII and Martin Luther never intended a full and permanent separation of communion.