Premise 1: A 'sampling distribution' of a statistic (e.g., a sample mean) is a piece of knowledge that tells us what we should expect a statistic to be (given some null hypothesis)

Premise 2: A bayesian 'prior distribution' is a piece of knowledge that we use to describe our degree of belief in a particular parameter of some model/hypothesis (e.g., a particular mean of our data?).

Is it incorrect to assume that a frequentist sampling distribution is just a prior on the mean value (or any particular statistic) of the null model?

If this isn't correct, what makes the sampling distribution different from a bayesian prior distribution?

Thanks for reading