synonyms - Do all “epicene” pronouns mean the same thing as one another?

There have been many pro­posed epicene or gen­der-neu­tral
pronouns

that have been pro­posed over the years and have re­ceived some level
of use. My ques­tion is: do all of them mean the same thing?
Are they synonyms for each other? Is it even pos­si­ble for
pro­nouns to have syn­onyms?

That is, if a per­son has in­di­cated that oth­ers should re­fer
to them with gen­der-neu­tral pro­nouns, is the choice of which
pro­noun to use (e.g. sin­gu­lar they, Spi­vak pro­nouns, thon,
etc.) a ques­tion of per­sonal pref­er­ence, style (e.g. per­haps
a spe­cific mag­a­zine de­cides to stan­dard­ize on us­ing thon

for all per­sons not iden­ti­fy­ing as “he” or “she”), or prag­mat­ics,
or is there a deeper is­sue of mean­ing?

For ex­am­ple, is there a pro­noun that refers only to trans­men,
and where use of the pro­noun to re­fer to peo­ple who are not
trans­men (e.g. women or cis­men) is to some ex­tent dis­cour­aged
or con­sid­ered in­cor­rect?

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Please note

<sup>This ques­tion is ob­vi­ously re­lated to the re­cent con­tro­versy
on Stack Ex­change, but is in­tended to be an in­de­pen­dent ques­tion
about the English lan­guage and not an at­tempt to bring the
con­tro­versy here. To be clear, I’m not ask­ing for opin­ions on the cur­rent
con­tro­versy. I’m ask­ing if there has been any in­di­ca­tion (e.g.
through re­search, or even ac­tivism) to in­di­cate that these
pro­nouns have dis­tinct mean­ings as op­posed to sim­ply be­ing
pre­ferred or des­ig­nated by dif­fer­ent com­mu­ni­ties, or

rec­om­mended based on so­cial, po­lit­i­cal, or reg­u­la­tory
rea­sons.</sup>