Naming & semantics: hilbert_series, multi_hilbert_series

[JohnAAbbott]

Last week we completed integration of the new implementations of Hilbert series -- thanks to @HechtiDerLachs !
Right now there are two interfaces: hilbert_series and multi_hilbert_series. What is the difference between these two functions?
If I recall well, multi_hilbert_series is more general but returns a result composed of laurent polynomials, whereas hilbert_series return normal polynomials (so the grading must be positive). Is this the only difference?
Would it make sense to rename multi_hilbert_series to something like hilbert_series_laurent (or other?)? Starting with the same prefix might be advantageous to users hunting for functions for computing Hilbert series.

This may be slightly related to discussion #2407