@ArnaudD. There are, IMO, some difference between e.g. real-analysis, abstract-algebra, and e.g. differential-geometry, algebraic geometry. For example, for real-analysis, it covers of course all introductory analysis, some might also uses it for question in measure theory. But if you go a little bit ahead, it seems unnecessary to use this tag for questions in PDE, harmonic analysis.... at some points there seems to be a cutoff for the real-analysis tag.
There are 384 questions tagged gre-exam. This appears to be a meta tag that I cannot really imagine anyone watching or searching for. I think it should be deleted.
From what I read there, this tag tag was in a different spirit. It was not tied to GRE, GMAT, CSIR, TIFR, etc. It was intended as "questions suitable for an exam". Which is rather vague and definitely opinion-based - so I am not surprised by bad reception of that particular suggestion.
The question is whether e should be a synonym of exponential-function. (Although at this point, cancelling the synonym would mean quite a lot of work in retagging older questions.)
Maybe we can edit the tag wiki and tag excerpt to make explicit questions about Euler's number per se can be tagged with exponential-function? (it's unclear at present that it is actually a synonym of e)