Hey there! I know anoneyemoose already responded with more information as well, but here's what we can add, too:
The therian community began completely separately from the otherkin community. The therian community started on alt.horror.werewolves in 1992, while the otherkin community traces its roots back to elven groups in the 1960's-1970's. Phytanthrope as a term was actually coined specifically by Darahagh of @liongoatsnake (AKA my partner system House of Chimeras) on a therian forum in 2013, while the fictionkin community started in 2001 through a webpage hosted on Otherkin.Net called Temple of The Ota-’Kin, where the predecessor term "otakukin" was coined. Theriomythic, another relevant term not included in the original list but which I'm going to mention because I love it, was coined in 2013 to be outside of or in-between otherkin and therian as a label, for people who felt themselves to animalistic and mythical but who did not fit comfortably into either term.
Nowadays, because of the ways these communities overlap and intermingle, many people use otherkin as an overarching umbrella term for all of these groups, but taxonomical arguments around sorting still exist aplenty because there's so many different models you can potentially use. If we go via history, then fictionkin would be under otherkin and phytanthrope could arguably be placed under therian; if we go via most common use, then they'd all be under otherkin; if we go via subcultural differences, they'd all be separate entirely! It can be tricky to navigate, and YMMV.
Some cool resources for community history, which includes more detail on what I've mentioned here:
A Timeline of the Therianthrope Community by House of Chimeras
A Timeline of the Fictionkin Community by House of Chimeras
A Timeline of Plant-Identified People in the Otherkin Communities by House of Chimeras
A Timeline of the Unicorn Community & Unicorns in The Otherkin Community by House of Chimeras
A Timeline of the Alterhuman Community by House of Chimeras
The Otherkin Timeline: The Recent History of Elfin, Fae, and Animal People by Orion Scribner (@frameacloud)
Addendums to Scribner’s The Otherkin Timeline by House of Chimeras
Otherkin Lexicon: A Multi-Lingual Dictionary of Jargon Used in the Communities of Otherkin, Therianthropes, and Other Similar Peoples by Orion Scribner
...and also House of Chimera's Website and Orion Scribner's Website more generally are just great resources. Just a heads up that my partner Orion's website is having some problems right now, so some links are down.
For other communities and terms you could consider to be a part of the alterhuman umbrella, you could check out some of the categories I have for the Alterhuman Archive? That'd include fictherians, fictionflickers, archetropers, endels, factkin, folcintera, othervague, people with paratypes, transspecies folks, vampires, otherkith, people with hearthomes, theriomythics, daemians, soulbonds, and tulpas. And beyond that, for things not listed as categories on there, there's also constelics, synpaths, and folks with kardiatypes, among others. That's just what I can think of off the top of my head.
