Having a distribution over possible coins isn't related to frequentism vs. Bayesianism, I don't think. In frequentism, you can ask, "If I have a whole bunch of mystery coins with different biases, what is the distribution of their biases, and for how likely am I to flip k heads in a row for each possible bias?" And in Bayesianism, that distribution can just be the prior/posterior distribution for a single mystery coin.