To add to what was already said here:
Confidence intervals and credible intervals are obtained by different means and they have different interpretations.
Intuitively, confidence intervals are obtained solely from the information encapsulated in the data about the unknown quantity to be estimated and are a frequentist statistics concept. In contrast, credible intervals are a Bayesian statistics concept and can incorporate not only the information present in the data but also any information about the unknown quantity to be estimated available before the data are collected (e.g., information available in the literature or from experts).
Both types of intervals are reported as a range of values (a, b), where a is the lower end point of the range and b is the upper end point.
Credible intervals have a more natural interpretation than confidence intervals.
For a 95% credible interval (a,b), the unknown quantity of interest is expected to lie in the range a to b with a 95% probability.
For a 95% confidence interval (a,b), if we were to repeat our study many, many times under similar conditions, we would expect that 95% of the resulting confidence intervals for the unknown quantity of interest would include this quantity. For this reason, we say that we are 95% confident that the unknown quantity of interest ranges from a to b. (Each repetition of the study would produce a sample of the same size as the one used to obtain the 95% confidence interval, but the samples would be different from one repetition to another, implying that the repeated confidence intervals would also be different. This repetition idea is crucial to understanding frequentist statistics concepts, but is usually something hypothetic we do in theory - in practice, we draw a single sample and use that sample to construct the confidence interval (a,b).)