An interesting comparison to make is with
Danbooru tags. They have five different tag categories for all the image posts in their database:
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artist tags: identify the creator of the post
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character tags: identify the characters in the post
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copyright tags: identify the anime, manga, game, novel, etc. associated with the post
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meta tags: describe things beyond the content of the image itself: e.g. "translated", "copyright request", "duplicate", "image sample", "bad id"
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general tags: describe the visual and factual elements in the image
So meanwhile, with the Mangadex manga tag categories, they're sort of like this:
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theme tags: describe the content of the manga: specific tropes or concepts
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genre tags: like theme tags, except more general and holistic (the distinction can be unclear, though)
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format tags: a mix between general tags describing the layout/presentation/structure of the manga (i.e. "anthology", "4-koma", "full color", "long strip", "oneshot") and metatags describing information that requires external knowledge and cannot be discerned just by looking at the content of the manga itself (e.g. "adaptation", "award winning", "doujinshi", "fan colored", "official colored", "user created", "web comic")
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content tags: a selection of theme/genre tags that would affect the age appropriateness of the manga (i.e. sex, violence)
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demographic: a specific selection of metatags relating to publication origin
(As for what the difference between a theme and genre is... I'm still not entirely clear on this. For instance, I think "supernatural" and "school life" are very clearly genres, not themes. But what exactly is a genre? What exactly is a theme? The distinction is so fuzzy! For example, take a look at the
most commonly used tags on AO3. If someone were to go through that list and classify each tag as either a genre or a theme, what would their decision algorithm be?)