What is the nature of the "assistant professor" position in India? In this recent academia.SE question, the questioner mentions that as an undergraduate they did research with an assistant professor.  That faculty member had a master's degree (only) at the time and has since moved on to be a PhD student at another institution.  

To my American eyes, it seems strange to have the positions of "graduate student" and "faculty member" intertwined like this.  In a comment, the questioner wrote


  Just to shed some more light on this, I come from India and here it is part of official policy to allow people with graduate degrees to rise to posts as high as assistant professor. I am not sure why this difference in academic practice has not come to the notice of admissions committees in the US in spite of the fact that thousands of Indian students have gone there over the years.


Well, I am the chair of a graduate admissions committee, and indeed this difference in academic practice had not come to my notice until now.  I would like to understand it better -- in particular:

1) What does this position entail?
2) Which Indian institutions and departments are (still) hiring assistant professors with masters degrees?
3) Can a master's degree assistant professor retain that position indefinitely?  Do they?
4) What percentage of higher-rank Indian professors did an assistant professorship between a master's and a PhD degree?



[Here follows more information about why I am asking the question and context about how what I know so far makes it sound different from the US.  It is not necessary to read this part or address it in an answer.]

In the United States there are so many PhDs looking for academic jobs that the days when someone without a PhD can teach advanced undergraduates at a research university or nationally ranked liberal arts college are almost completely past (more precisely: there are still some such people, but they were hired a long time ago).  However there are other institutions of higher learning in which faculty can teach with master's degrees, and I have known some cases.  (I suspect that the window for this is shrinking as well, as we continue to produce many more PhDs desiring academic positions than the market can bear.)  

But I don't know of any American institution of higher learning in which a faculty member with a master's degree can be an assistant professor but have no higher rank.  Moreover, the type of institution which has tenure track faculty with master's degrees is quite different from the type of institution in which (i) faculty do research with their undergraduates and (ii) send students to graduate school.  (I tried to choose language to minimize the elitism / academic caste-ism in that last assertion, but that minimum is unfortunately positive, since American academia is elitist...)
Indian universities are not very homogeneous, but it may be helpful to divide them into two categories:

(1) National institutes/universities:The top-tier universities with highly competitive admissions and recruitment processes. A commonly stated figure is that 1% of applicants make it to these institutes, though I think it may now be closer to 10%, with more institutes opening in recent years. In this category, an Assistant Professor must hold a PhD and have 3 years post-doctoral experience.

(2) Other universities: One requires a Master degree and must qualify a national-level entrance exam to become Assistant Professor. Yes, one may continue in this post without a doctorate, though in practice this is rare. Full professors (and perhaps associate professors too- not sure on this) require PhD.

The second category might appear strange from a US perspective. It may help to recognize that these universities tend to place pedagogy over research. This is an outcome of having a large population and limited employment prospects without a college degree.