This is something I have thought about for a long time. I certainly can't speak for the people at LC who established these subject headings or the folks who are using them now, but here is my view (please bear with me, it's a long answer):
"Series (Publications)" is broader than "Monographic series" (it has 550 $wg from the former). "Series (Publications)" has a 550 from "Serial publications" without a $w g.
"Monographic series" isn't defined in the RDA glossary, but "Series" has two definitions there. The first, which is the more relevant to this question, says
group of separate resources related to one another by the fact that each resource bears, in addition to its own title proper, a collective title applying to the group as a whole. The individual resources may or may not be numbered.
Two things to note about this definition: (1) each resource has both an individual title and a collective title (not just some of them); and (2) a Series is not necessarily a Serial (continuing resource).
MARC also defines "Series," or we have allowed it to. It could be anything one can create a series authority record for, or anything that one can legitimately put in the 490 and 8XX fields of a bibliographic record. What are those things? The authority field 008/12 gives 4 options:
$a Monographic series [a type of serial]
$b Multipart mongraph
$c Series-like phrase
$z Other [often used for Periodicals with (some or all) analyzable issues]
Looking at these, right away it's clear that "Series = anything that can get a SAR" doesn't fly. A Series-like phrase, by definition, is not a Series; and a Periodical with some analyzable issues isn't a Series because it probably doesn't fit the RDA definition (each part has its own title and a collective title; unless the Periodical has ceased and we can examine every issue, we can't tell). Also, if we label a Periodical as a Series, that is potentially confusing (to anyone who isn't aware of the analyzable issues, because their institution doesn't own them or doesn't analyze them). It can appear that there are two different resources with the same title: one a Periodical and the other a Series.
The notion that "Series" is equivalent to MARC Series Treatment has been practical in the MARC cataloging environment, but I think as we develop ontologies for linked data we need to pry ourselves away from it. "Series (Publications)" may still have a place
as a fuzzy term because it is used by publishers both for Monographic series (scholarly publications, usually) and Multipart monographs (popular and children's publications, commonly; also complete works of an author).
Today, people may be assigning "Series (Publications)" along with a more specific term, "Monographic series," "Multipart monograph," or "Periodical" to resources because they understand the problems with the definition of Series.
I have suggested that we narrow the definition of Series to include only Monographic series, because Monographic series alone really fits the definition of Series (where every part is analyzable). For a Monographic series, the individual title is the main
focus; the series title is a sort of publisher's promotional glue. For a Multipart monograph, the collective title is often (usually?) the main focus, and all of the parts do not need to have their own titles. If the definition were narrowed in this way,
then a Series would always be a Serial.
If the definition of Series does evolve to exclude analyzable Multipart monographs and analyzable Periodicals, they can be described as having Whole/Part relationships. Series (Monograph series) would simply have a specific type of Whole/Part relationship. Currently, almost any Whole/Part relationship can be called a Series relationship.
My suggestion does not take into account the broader/common usage of the term "Series" by publishers. Opinions may differ as to whether that is a deal-breaker.
I hope this is helpful. Maybe 'way more than you wanted to know!
Mary Jane Cuneo
Senior Serials Cataloger/NACO Contact
Jacob Burns Law Library
George Washington University