How to figure out whether a Masters degree is a "Professional" or "Research" degree? How to figure out whether a university-program is offering Professional Masters degree  or "Research" Masters degree?

Are all taught Masters degree programs professional programs?
The main difference is that research MS degrees require a thesis, which describes the student's research, while professional/taught MS degrees do not.

There are several secondary differences as well.  Professional/taught MS programs are cash cows; their enrollments are generally higher, their admissions criteria are generally lower, they almost never offer financial support, and students are generally treated like cattle.  Research MS programs generally have smaller enrollment, because the students require more individual attention, and therefore higher admission standards; some research MS programs offer financial support in the form of assistantships or even fellowships.  In many departments, there is an easy transition from a research MS program into the PhD program; transitioning from a professional/taught MS program into a PhD program is almost impossible.

Of course, these answers are very crude approximations.  The actual difference will vary significantly between departments.