Some background
When I was a preteen and first got into the fourth generation of My Little Pony, I didn't do so via the TV cartoon, but rather through fan content (incl. roleplays) and what we can call "subcultural osmosis" through said fan content. In the current moment I can say a similar thing about Touhou series: that I have listened to plenty of fan-made songs and seen fan-made animations and seen memes and listened to fan discussions and read fan wikis and just generally absorbed a decent amount of its lore through osmosis, but still haven't played any of the games.
And this gets into what fan content vs official content actually is. I like the analysis that fan content is unpaid labor which generates value for official content: in other words, that the mechanism of copyright allows some works concerning the same world or characters to be given an artificially inflated "prestige", while other works taking place in that universe exist in an area of being strictly illegal, but allowed to exist by rightsholders insofar as they help maintain this relationship to their benefit.
About ten months ago @doublepepperoni@hexbear.net posted a thread asking for alternatives to "intellectual property" (IP) or "franchise" as a way to describe long-running established fictional universes, saying that "IP" and "franchise" sound like terms used by copyright lawyers and marketing ghouls. This was where I proposed the use of the term "cycle" for this purpose, as this term is already used to refer to "a series of poems, songs, or other works of art" or "a group of stories focused on common figures".
Other people said things like "series" or "corpus" or "canon" or "universe" or "mythos" or whatever else, but I still favor "cycle" myself. Because although at first I said that it would maybe be a bit peculiar to speak of Sailor Moon in the same terms as ancient folktales passed down orally for generations, ten months later I now say, "Why the Hell shouldn't we?" — like, what is to say that after copyright is abolished, that centuries from now, people won't be passing down stories of the Sailor Guardians in the same way as Sinbad and Aladdin?
Since "cycle" can cover stories with the same characters, stories set in the same location or universe, or by the loosest definitions basically any set of creative works sharing anything in common, I'd say that "cycle" covers our bases more comprehensively than other terms. And yeah, if we are to use "cycle" instead of "franchise" or "IP", we could just say "Sailor Moon cycle", but where is the fun in that? Why not commit to "the bit" and come up with brand new names for things based on our conventions for naming collections or sets of folk tales?
So that's basically why I made this post.
Some common words we might see in these types of titles other than "cycle" are "tales", "matter" (implies a cycle about a place, especially a country), the suffix -iad, or indeed just "mythos". It depends on what you think works best.
So, to start with, I'm gonna rename the things namedropped in the "Some background" section:
My Little Pony G4 → The Matter of Equestria
Touhou series → The Matter of Gensokyo
Sailor Moon → Tales of the Sailor Guardians, or if we prefer a pun, The Lunar Cycle (though that name could certainly be applied to many other cycles)
We might also say...
Non Non Biyori → The Matter of Asahigaoka
Star Wars → The Matter of the Galaxy Far Far Away
Half-Life and Portal series → The Black Mesa Cycle
What sorts of names can you come up with?
Sent from Mdewakanton Dakota lands / Sept. 29 1837
Treaty with the Sioux of September 29th, 1837
"We Will Talk of Nothing Else": Dakota Interpretations of the Treaty of 1837
Tales of Son Gokuu and earth's warriors --- DBZ (I think this is how it works).
Hell yeah brother
Sent from Mdewakanton Dakota lands / Sept. 29 1837
Treaty with the Sioux of September 29th, 1837
"We Will Talk of Nothing Else": Dakota Interpretations of the Treaty of 1837
Funny enough DBZ already has a cool name for its subsections, Saiyan Saga, Frieza Saga, Cell Saga etc