Neither of them have to be. All exchanges take place in pairs; one holding is exchanged for another. Buying BTC with dollars is (USD, BTC); buying Microsoft is (MSFT, USD); buying EUR with dollars is (EUR, USD).
Nothing prevents you from pricing Microsoft stock in BTC or BTC in EUR or Etherium.
The holding as such, however, is only a fiat holding when it is in fact either a (wad of) cash equivalents and/ or a bank balance.
There isn't a person on earth for which there is only two types of relevant holdings, in either USD or BTC. A person that (seriously) considers acquiring a crypto holding, such as BTC, is most likely choosing between other crypto currencies, gold or silver, primarily. Even more likely, they're merely FOMO-speculating as a complement to plain stock holdings.
The fact that a number of you don't seem to understand this should call your competency into question.