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It's not specific to dragons, but some of this is tied to High Fantasy versus Low Fantasy.
In High Fantasy, fantastic creatures tend to be legendary, extremely long lived, divine, explicitly magical, that sort of thing. A dragon might be an ancient sorcerer who hoards magical artifacts.
In Low Fantasy, if there are fantastic creatures, they tend to be closer to ordinary animals that happen to have noteworthy abilities, but usually restricted to abilities that MythBusters might deem "Plausible". Dragon firebreathing, for example, could be seen as an extension of abilities that real animals have, like the bombaridier beetle and formic acid-spraying ants.

When a story features dragons, there’s a large gap between how grandiose (for lack of a better word) their portrayal is. For some stories (ASOIAF, Monster Hunter, Harry Potter), they are portrayed as animals. Magical animals, for sure, but still simply creatures; for other stories (The Hobbit, Sekiro, Dragon’s Dogma), they are intelligent creatures who either are themselves divine or work closely for those who are. Most stories fall somewhere in the middle, but even this can vary. Is there a trope specifically for this scale? There’s the ‘dragons are divine’ trope, and the ‘our dragons are different’ page goes over a lot of this, but I feel like I might be missing something. If this doesn’t have its own page, does it warrant one?