Thanks.
Monastery is a stretchable term, some monasterys Held only a single Monk and Not every "Monastery" had a church, either inside, attached or seperate to the building..a lot only had (and still have) a chapel, a room set aside for prayer/Meditation and could be used as an oratory, ie; it could be used in the way a classic church would be with a Speaker talking to the congregation.
In the case of my "monastery" it could theoretically be inside the main building or in a crypt or seperate from the main building.
A cloister isn´t necessarily part of a monastery....it´s a metonymic Name (figure of speech) for a Monastery *
A cloister (from Latin claustrum, "enclosure") is a covered walk, open gallery, or open arcade running along the walls of buildings and forming a quadrangle or garth
A monastery generally includes a place reserved for prayer which may be a chapel, church or temple, and may also serve as an oratory.
Generally as in, not always
* I know that in German a Monastery is called a Kloster (from claustrum, enclosed space) but what in english is termed a Cloister, the enclosed walkway is called in german a Kreuzgang.
Etymologically correct is;
Monk(s) living/working/praying etc area - Monastery (monasterios from –monazein
"to live alone")Enclosed walkway around a building, church/temple or monastery - Cloister