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You may be looking for Episode Tag, a type of fanfic.
A formal set of tags may be a "taxonomy" or "controlled vocabulary". Most fandom tags are informal and uncontrolled, known as a "folksonomy".
Archive Of Our Own combines these in a complex and labor-intensive but effective Tag Wrangling process, which allows creators to tag as they please but then marks many tags as synonyms for a canonical tag. This allows readers to find or filter out fandoms, pairings, and topics without having to indicate each one individually. Other tags are "free form" and not included in the wrangling system (see Unhinged ao3 tags for some unique examples that somewhat follow tumblr tagging styles). Early versions of this system were inflexible and frustrating, partly for technical reasons but also volunteer and policy issues, leading to extensive AO3 Tagging Policy Debate.
Tumblr Tagging is completely free-form and idiosyncratic. Hashtags are used for finding fandom discussion, identifying fanworks, post blocking, and commentary. Tumblr tags are visible in post notes but no longer automatically retained during reblogging, which makes them ephemeral and personal.
Some Very Early Fan Comments
A discussion from 2002:
I wonder why people would read a story in a genre they don't care for, then take the time to let the writer know that sure enough, they didn't care for it. That would be like me going to a restaurant, ordering a slice of cherry pie, then asking that the chef be brought out so I can say "I don't like cherry pie, and I didn't like yours either." To continue this analogy into its usual fannish outcome, the chef would say "Well gee, lady, why did you order it?" And I'd say, "Are you questioning my right to order cherry pie?" <Chef walks away, puzzled>
- I have actually been thinking about archives recently. In those days when I was looking for a second fandom for reasons I won't bore anybody with right now, I tried a lot of stuff about shows I hadn't seen for years but had kinda liked when I did; one of these was Forever Knight. I don't know what the archive situation is over there now, so if anybody here is a FK fan and knows differently, feel free to update me. But the one I visited had *hundreds* of stories. Dozens of pairings. Many many time periods (it's a vampire cop show, for those who have never heard of it). AUs. Romance. Horror. Humor. Death and undeath.
- The stories were listed down one interminable page, and if there was any organizing principle whatever, I have forgotten it. I'm sorry, but that's just not workable. I clicked on a couple of things in a kind of numb despair, but I was just *overloaded.* I couldn't read anything.
- Someday, unless online SH fic dies out, we will have this problem.
- A good big archive ought to be a *draw* for new fans. I've dipped into Sentinel and Due South lately, and I adore their archive search engines. Of course, they are fandoms that do use headers to a degree which obviously makes some of us really uncomfortable.
- But --stop me, oh technical goddesses, if I err here-- there's no law that says the only things you can search are right out there *visible* in the story listing. Would it not be possible for us to get a search engine that read META tags? Then those who didn't want to know could surf the author or title listings, pick a section (beginning with A, right?) and never be bothered by the pesky labels (they are invisible to someone normally viewing the page), while others could look up BDSM, OCs, FT, NC-17 and be happy too.
- Putting in a lot of META tags in a lot of stories would be a big and tiresome job; for authors who are not reachable to ask or who don't want their stories to be searchable in that way, we'd have to do without; and anyway somebody may think this is a highly stupid idea. But I just thought of it, and if we might think of it seriously we should probably begin *before* we have gazillion stories in a long, long, long list. 
- The past, present, and hopeful future for tags and tag wrangling on the AO3, Archived version (2012)
- The fanfiction community has made it very clear that it hates me (May 23, 2022)
- The Strange Case of Stichomancery by J.D. Riley (Aug 16, 2022)
- from Venice Place Mailing List, quoted anonymously (1 Feb 2002)