The main difference between Monastery and Priory is that the Monastery is a complex of buildings comprising the domestic quarters and workplace(s) of monks or nuns and Priory is a religious house governed by a prior or prioress
A monastery is a building or complex of buildings comprising the domestic quarters and workplaces of monastics, monks or nuns, whether living in communities or alone (hermits). A monastery generally includes a place reserved for prayer which may be a chapel, church, or temple, and may also serve as an oratory, or in the case of communities anything from a single building housing only one senior and two or three junior monks or nuns, to vast complexes and estates housing tens or hundreds. A monastery complex typically comprises a number of buildings which include a church, dormitory, cloister, refectory, library, balneary and infirmary. Depending on the location, the monastic order and the occupation of its inhabitants, the complex may also include a wide range of buildings that facilitate self-sufficiency and service to the community. These may include a hospice, a school, and a range of agricultural and manufacturing buildings such as a barn, a forge, or a brewery.
In English usage, the term monastery is generally used to denote the buildings of a community of monks. In modern usage, convent tends to be applied only to institutions of female monastics (nuns), particularly communities of teaching or nursing religious sisters. Historically, a convent denoted a house of friars (reflecting the Latin), now more commonly called a friary. Various religions may apply these terms in more specific ways.
A priory is a monastery of men or women under religious vows that is headed by a prior or prioress. Priories may be houses of mendicant friars or nuns (such as the Dominicans, Augustinians, Franciscans, and Carmelites, for instance), or monasteries of monks or nuns (as with the Benedictines). Houses of canons regular and canonesses regular also use this term, the alternative being “canonry”.
In pre-Reformation England, if an abbey church was raised to cathedral status, the abbey became a Cathedral Priory. The bishop, in effect, took the place of the abbot, and the monastery itself was headed by a prior.
housing monks or others who have taken religious vows
A monastery or convent governed by a prior or prioress.