Following the line of the synonymization between projection and coordinate-system, I would agree to synonymize projection-mathematics and reprojection-mathematics to coordinate-system as well.
Mainly because I think they should be synonymous with projection.
The terms are not synonymous. However, I don't think synonymous tags should necessarily refer to synonymous terms.
What I would find useful is to add in the definition of cordinate-system that the tag:
also applies to projective geometry and coordinate system transformations.
I think that it would be resolved that when a user writes projection in the field of tags, he/she note that everything related to projections and reprojections is labeled as coordinate-system, which after all is very useful to group in that way all the questions that refer to the coordinate systems in which geographic information is analyzed and represented.
It occurs to me that the description or definition of what a coordinate system is, is not enough to describe the tag:
A reference framework consisting of a set of points, lines, and/or surfaces, and a set of rules, used to define the positions of points in space in either two or three dimensions.
And that adding a phrase referring to cartographic projections and coordinate system transformations could help describe the tag and its synonyms.
It may be convenient to open a new question about this idea. For now it is raised here and in the chat.
A wiki edit was submited for approval, wich includes the phrase:
This tag also refers to cartographic projections and coordinate system transformations.