What is the difference between a monastery and a convent?

Like many words, we can denote a strict sense, and a more relaxed colloquial sense. We can also note that the meaning of the words have changed a bit over time. 
 
The word monastery originally came from the Greek word monazein which means, “to live alone." In the earliest days monastics, (both men and women) went to the desert to live a largely solitary life in separate dwellings. However, many of them in a local area came to share some common buildings for prayer and eating. Over time many came closer together, and eventually were housed under one roof, though the monks and monastic sisters still tended to keep long hours of silence. Thus they lived in a relative, if not physical solitude, coming together also for communal prayers, meals and necessary community deliberations in the shared chapel, refectory, and chapter hall. 
 
Today the word “monastery” has tended to be used only of communities of men, while communities of women have tended to have their dwelling denoted as a “convent” or “cloister.” But, technically, there are women’s communities whose domicile is most properly termed a monastery. 
 
The main difference that the term “monastery” is meant to signify is that those who live there, live “alone” or apart from the everyday world. Their prayer is centered in the monastic community. Generally too, their work or apostolate is also centered there, rather than out in the community or world. Some enclosures are strict, others less so, but the concept of dwelling apart is key. 
 
“Convents” and religious houses, however, tend to house religious men and women who do not live and work in such isolation from the everyday world. Perhaps they work in education, hospitals or other external places during the day, but then return and live in community, sharing meals and prayer and other aspects of common life. The word “convent” comes from a Latin word which means “to convene or gather,” and is less inclusive of the concept of solitude contained in the word “monastery.” 
 
Historically, communities of men and women have used different terms to indicate “conventual” settings. Women’s communities have used terms like convent and nunnery, whereas for the men’s communities terms like priory or friary have been used. 
 
Nevertheless, and despite a variety of adaptations, the fundamental distinction to be observed is between communities (male or female) that live in some solitude (monastic) and those which interact more directly with the everyday world (conventual).