Aha! I am working on a not-M.Div. Master's degree. I can answer this!
(I don't know about the ecclesiastical degrees, STB, STL whatever.)
An M.Div. is a professional degree working towards ordination. It generally takes three years of full-time studies.
MAs generally take two years of full-time studies.
There are professional MAs that are geared towards working in church ministry but not in an ordained capacity. Master of Arts in Youth Ministry, that sort of thing.
There are also two-year degrees, which are more academic than professional. The really confusing thing is that just about every seminary/divinity school offers these but they're often called different things! I'm working on a Master of Arts in Religion. A lot of schools call essentially the same thing an MTS (Master of Theological Studies). At my school there are a bunch of different programs that all get different letters. Master of Arts in Biblical Languages (MABL), Master of Arts in Theology (MATH), etc. Why in the world not just give us all MAs with different "majors"? A lot of schools do that but mine does not, no idea why. These degrees do not prepare for ordination and are often a stepping stone to a PhD and a life in academia.
A Th.M. is a weird beast. It is a one-year Master's degree FOR PEOPLE WHO ALREADY HAVE AN M.DIV and are either (1) trying to develop a specialty in a particular field, or (2) gluttons for punishment. ;)
I looked at getting an M.Div. but found that at my school the M.Div. program is so structured I wouldn't be able to develop a specialty in anything, which was missing the point of what I'm trying to do. For me the MA program lets me focus in my particular area of interest, which is my whole point of doing this. At other schools the M.Div. program can have more space for electives. It just varies.
For an academic career (not sure if this is what you are looking for) you will need a Ph.D. Sometimes, Ph.D. programs will be more receptive to a candidate with an MA than an M.Div., as an M.Div. can be seen as a professional program rather than academic, and less rigorous. But this really varies from seminary to seminary. In some they are very different tracks. In others the M.Div. people take most of the same classes, just more of them!
Hope this helps.