What is equivalent degree of Masters by research degree in the USA?
In my experience, there isn't a separate degree in the US for achieving your Masters degree through research. In fact, in many places, that's the only way to do so. At the university where I received my Masters degree, you had three options, all of which granted the same degree:


Coursework - Take something like 30 course hours.
Coursework + Project - Take fewer hours (around 20 - 24) and do a larger project than a normal project course.
Coursework + Thesis - Take fewer hours (around 20 - 24) and do a smaller thesis than a PhD.


Many universities don't have of the options and just have #3.