"Institutes of consecrated life" are canonically erected by competent church authority to enable men or women who publicly profess the Evangelical Counsels by religious vows or other sacred bonds, "through the charity to which these counsels lead to be joined to the Church and its mystery in a special way" (cf. canon 573.2 of the 1983 Code of Canon Law), without this however making them members of the Church hierarchy. Such institutes are generally called "religious orders" (for instance, the Order of Friars Preachers; but also, the Society of Jesus and the Sisters of Charity).

A "religious order" is one in which solemn vows are taken by members, and that follows an accepted rule. Institutes in which members take only simple vows are religious congregations (a "clerical congregation", if primarily made up of priests and oriented toward priestly work; a "lay congregation" if not). (Canon 588 -- Note: this is not canon 588 of the Code of Canon Law 1983, so this paragraph needs to be duly revised).

A monk (Greek: monachos, Latin: monachus) is a person that leads the "monastic life" in a "monastery". Nowadays it tends to be wrongly assumed that it signifies someone living in community. From early Church times there has been a lively discussion of the meaning of this term (Greek: monos alone), namely whether it denotes someone living alone/away from the rest of society, or someone celibate/focused on God alone. St Benedict understood it as meaning the latter, namely a celibate dedicated to God, as becomes clear from the fact that he considers a hermit to be a kind of monk (Rule of St Benedict, ch. 1).

A monastery (Greek: monasterion) is a place where a monk lives and works, and may be home to any number of monks, one or many. Often a monastery of one is, however, called a "hermitage".

The term "nun" (Latin: nonnus) has come to be used exclusively for female monks. In English the term "nunnery" is popularly used to denote the dwelling of a community of women. In recent literature one may also find the gender-inclusive term "monastics". Benedictines, Carthusians, Cistercians and Trappists are examples.

A "Friar" is a male member of one of the mendicant orders (principally, the Franciscans, Dominicans and Carmelites).

The term "Religious" (as in, "he/she is a Religious") is commonly used to refer to a consecrated person, a person in religious vows.
Priests in vows retain their usual title of "Father", and "Reverend Father". With a few exceptions (see Jesuits for example), all men in vows who are not priests and therefore to be addressed as "Father" are addressed as "Brother". That is to say, all monks are brothers, but not all brothers are "Fathers".

Women are addressed as "Sister". Benedictines have traditionally used the form of address "Dom" for men and "Dame" for solemnly professed nuns. All nuns are sisters, but not all sisters are nuns. The term "nun", broadly speaking, used to be reserved for women in solemn vows and in religious institutes that are subject to Papal Enclosure, the term "sister" for women in simple vows and in other religious institutes. Today this distinction has become blurred. Some women superiors are properly addressed as "Mother", and "Reverend Mother".

Source: http://en.wikipedia.org/wiki/Consecrated_life(Catholic_Church)

Institutes of consecrated life are regulated in canons 573-746 of the Code of Canon Law. Canon 573 tells us that:

§2. The Christian faithful freely assume this form of living in institutes of consecrated life canonically erected by competent authority of the Church. Through vows or other sacred bonds according to the proper laws of the institutes, they profess the evangelical counsels of chastity, poverty, and obedience and, through the charity to which the counsels lead, are joined in a special way to the Church and its mystery.

Is the Saint Benedict Center in Richmond, New Hampshire an Institute of consecrated life "canonically erected by competent authority" within the Church? The Diocese of Manchester has already addressed this: "..the Saint Benedict Center has no permission or authority to exercise any Ministry on behalf of the Roman Catholic Church in New Hampshire." (The Rev. Edward J. Arsenault, Moderator of the Curia for the Diocese of Manchester, to Mrs. Terri O'Rorke).

Additionally, it must be noted that there is no such thing as a legitimate expression of the Catholic tradition that is not in union with the Holy Father. The SBC refuses to accept the Magisterial teaching of the Catholic Church regarding the well-known axiom "Outside the Church there is no salvation" as outlined in Nos. 846-848 of the Catechism of the Catholic Church.