The difference between Bayesians and Frequentists is in the loss function that they attempt to minimize.
Bayesian loss functions assume a constant dataset and sums across one's hypothesis set.
Frequentist loss functions assume a constant hypothesis and sum over across possible datasets.
https://en.wikipedia.org/wiki/Loss_function
Really though this is false dichotomy, as it's perfectly possible to be both a Bayesian and a Frequentist by using a loss function which sums over both one's hypothesis set and across possible datasets.
The difference between Bayesians and Frequentists is in the loss function that they attempt to minimize.
Bayesian loss functions assume a constant dataset and sums across one's hypothesis set.
Frequentist loss functions assume a constant hypothesis and sum over across possible datasets.
https://en.wikipedia.org/wiki/Loss_function
Really though this is false dichotomy, as it's perfectly possible to be both a Bayesian and a Frequentist by using a loss function which sums over both one's hypothesis set and across possible datasets.