【Cloister】 and 【convent】 are general terms denoting a place of retirement from the world for members of a religious community; they may apply to houses for recluses of either sex. In such use 【cloister】 stresses the idea of seclusion from the world; 【convent】 , of community of living.
Basically a 【monastery】 is a 【cloister】 for monks; in actual use it is often applied to a 【convent】 for men or occasionally for women who combine the cloistered life with teaching, preaching, or other work.
【Nunnery】 , which specifically denotes a 【cloister】 for nuns, is often displaced by 【convent】 with the same specific meaning. A 【monastery】 or 【nunnery】 governed by an abbot or an abbess is called an 【abbey】 ; by a prior or prioress, a 【priory】 .
A 【priory】 is subordinate in rank to, but often independent of, an 【abbey】 .