In my attempt to learn Georgian, an agglutinative language of the South Caucasus, I have learned that it has both case endings *and* postpositions.

I also have some familiarity with Korean and Japanese which are usually analysed as having postpositions (as one subclass of their particle class) but not as having case endings.

When linguists study a new language hitherto lacking any tradition of grammatical analysis, how do they determine whether the language has either or both of these features, and which morphemes belong to which category?

Also when looking at a well studied language are there easy ways to tell the difference between the two or is it at least partly due to the accepted existing analyses?