While it is true that monasteries have often been repurposed for use by friars, no Dominican - no matter what building he lived in - would refer to himself as a monk.
Some disagree with you???
Dominikanski Samostan Campground (Dominican Monastery)
This campground east of town near the Dominican Monastery has limited space (70 sites) and is run by the monks. Exceptionally popular because of its location near the sea and its well-kept facilities, it is always full. However, if you are inclined to walk around in a state of skimpy dishabille, this is not the place for you. The site is posted with dress-code signs.
Read more: http://www.frommers.com/destinations/brac/H52473.html#ixzz0u3wInx4Z
http://www.lindenopnuns.org/page6/files/0e793987f1e2cad3236c10369eeefac1-2.html
And of course, since nuns are not ordained preachers like the Dominican friars, they live contemplatively. The usual term for such a building is a convent but it has become more common recently to call convents monasteries.
However, friars do not live contemplatively as monks do, spending all their time on monastery property solely in the company of other vowed religious. They spend their days in the world doing the work of their order. In the case of the Dominicans this means teaching and preaching in schools and churches and universities.
Reading the Dominican rule of life and comparing it to the Benedictine rule would illustrate the difference between a friar and a monk.