Master of Research (MRes) schools in the U.S.?
I've never seen the term "Master of Research" used in the US.  Many master's degree programs in the US do include a significant research component (either a thesis or project) while other master's degree programs consist entirely of coursework.  In either case, the degree can be called an MS (Master of Science) or MA (Master of Arts) degree.   

In programs that do include a thesis, the thesis might be 6 out of 30 credit hours in the degree program.  This is nominally 20% of the program but in practice students often spend much more than 20% of their time on the thesis.  In my experience in mathematics, 3 semesters of course work plus two semesters of work on the thesis is more typical.