if for fiat it's the central bank governor for a country that decides the local daily currency price against the other fiat currencies
The exchange rate of fiat currencies is not centrally defined either. Yes, some fiat currencies are pegged to another, giving a fixed predefined exchange rate. But that also only lasts until the peg is lifted. Some currencies may even have an "official" exchange rate and a black market exchange rate. However for the most part even the value of governmental fiat currencies are just free-floating relative to one another, depending on market forces which can only be indirectly influenced by governments (e.g. by printing more money or the buying / selling of foreign currency reserves). Then of course, there's factors such as goverment stability and wars, as mentioned by dkbit98.
Additionally, you’ll notice that bitcoin price will vary somewhat between different Exchanges, but not entirely. The specific liquidity on an Exchange affects its price.
The availability of fiat on and off-ramps also seems to play a role. Exchanges that offer limited or no options for direct fiat withdrawal usually have a slightly higher exchange rate than those that make it easier to withdraw fiat.