The difference of Bayesian credible interval (BCI) and the frequentist confidence interval (FCI) is well explained with a nice example in this answer. Here is my own summary of the situation in the example. There are four kinds of jars. All jars contain the same number of cookies. Each cookie contains some chocolate chips. Each kind of jar has a fixed distribution of the number of chips in a cookie but different kinds of jars have different distributions. Now I have a jar on my desk delivered by my friend but I don't know what kind of jar it is. I draw a cookie from the jar and count the number of chips in it. Now I want to infer what kind of jar I have. I want the inference to be right in 70% of the case. BCI and FCI are different in this example as explained in the answer.
Let's modify the situation. Now I don't have a jar on my desk currently. Tomorrow my friend will pick up a jar and bring it to me. So the kind of jar is not an unknown fixed value. It is not fixed yet. To Bayesians, the modified situation is actually equivalent to the original situation. We just have the same information on the jar. However, for frequentists the two situations are different each other. In the original example, I think that the ensemble of virtual experiments of a frequetist is a repetition of the drwaing a cookie from the jar on the desk. In the modified example, I think that the virtual experiment must also contain my friend's picking up a jar. So in this case, the frequentist must "assume" a model of the pick up procedure and this amounts to a Bayesian's prior in the original example. So finally, in the modified example, BCI and FCI are the same and it is identical with the BCI of the original example.
Am I right? Or did I misunderstand something?