There are at least a half-dozen types of Catholic religious orders:  mendicants, monastics, canons regular, clerics regular, clerical religious congregations, and lay religious congregations.

Mendicants

Mendicants take a vow of poverty but extend that to not owning property at all, neither individually nor collectively.  Franciscans, Carmelites, and Dominicans — what I conventionally think of as “friars” — are examples of Catholic mendicant orders.  In an ultimate sense, mendicants are beggars. (Theravadan Buddhist monks are mendicants.)

Monastics

The monastic orders — e.g., the Carthusians (of the Charterhouse) — do not take ordination and are tied to a place, their monastery.  This is probably the best known type.  (It’s parallel to many Mahayana Buddhist monastic orders.)

Canons Regular

This is where the complexity of Catholic religious orders really takes off.  Canons Regular, like monastics, are tied to place and take vows of poverty and chastity and obedience.  But they’re ordained as priests (canon=clerk=cleric=priest) and they serve in ministry.

Clerics Regular

Clerics Regular are also priests, but they’re tied more to their order than to their monastery.  Jesuits are Clerics Regular.

Religious congregations

Religious congregations (lay and clerical) are distinguished from other orders by their type of vow; members of religious congregations take simple, not solemn, vows.  The distinction between the two types of vows is pretty obscure to me; fortunately, the Catholic Encyclopedia of 1913, incorporated into Wikipedia, has details.