Monastic orders
"The first race of monks is that of the Cenobites, that is, those who live in a monastery, and fight under a Rule and an Abbot." (Rule of Saint Benedict; chapter 1)
"The second species is that of the Anchorites or Hermits. ... / ... they leave the ranks of their brothers to engage in the single combat of the desert ..." (Rule of Saint Benedict; chapter 1)
The vast majority of monastic orders follow the founding precepts of Saint Benedict.
These orders mainly include:
• The Benedictines
• The Cistercians - "Bernardins"
• The Cistercians - Trappists
• The Carthusians

Mendicant Orders
The mendicant orders are so called because of their characteristic which was to “beg,” that is to say to resort humbly to the economic support of the people to live the vow of poverty and to devote themselves to their mission of evangelization. Their members are not called monks, but designated by the term "Brothers" or "Religious."
These orders mainly include:

Military and hospital orders
Military orders
Born of the crusade, dedicated to the defense of the Holy Land or to the Reconquest of the Iberian Peninsula, military religious orders were established, from the 12th century, far from places of combat against the Infidels, with networks of establishments in all of the medieval West.
Hospital orders
The aim of the hospital orders was to receive and care for travelers, pilgrims, the poor and the sick.
These orders include for example:
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The Order of Saint John of Jerusalem (hospital / military)
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Order of Teutonic Knights (Hospitaller / Military)
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The Antonines (Hospitable)
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The Hospitaller Order of Saint John of God

Different orders

In the Christian tradition, religious orders are associations of men or women who endeavor to follow Christ in an evangelical life. Members are bound publicly, or sometimes in private, by vows of poverty, chastity, and obedience in order to lead a consecrated life.
The main monastic or mendicant orders have all been in charge of breweries or at least a source of inspiration for brewers, and have left such deep traces that we still find many references to their beers in our time. Some monasteries are still brewing today.