Most members of Catholic religious orders are not monks, and superiors general are reliably unimpressed when told they are.
The thirteenth century produced the friars, and they were designed against the monastic model at almost every point. Where a monk vows stability to one house, a friar belongs to a province and can be sent anywhere in it or beyond. Where a monastery is endowed with land, the early mendicants refused endowment and begged. Where monasteries were founded in the countryside, friars went into the new cities, because that is where the population and the heresies were. Where a monastery is autonomous, the mendicant orders built a genuine command structure, with provinces, chapters and a superior general.
They were bitterly opposed at the time. Bishops objected to preachers operating in their dioceses under someone else's authority; university faculties objected to the chairs the Dominicans and Franciscans took; the secular clergy objected to the loss of funeral and confession income.
The sixteenth century added clerks regular, who dropped choral office and monastic habit altogether in favour of mission, education and administration, and who were organised more like an army than an abbey.
The largest group in numerical terms is different again: congregations of apostolic life, overwhelmingly of women, whose members take simple rather than solemn vows and who ran the schools, hospitals, orphanages and nursing services that constituted the largest organised welfare provision in much of the world for two centuries. Their history includes a long conflict with church authority, which repeatedly forced women's communities into enclosure against their founders' explicit intentions on the grounds that unenclosed religious women were improper. That restriction was not fully lifted until the twentieth century, and the institutional damage done in the meantime is well documented.