This is a note for me.
Confidence intervals: “Are the observed data x reasonable given the hypothesised values of θ?” == P(θ| x)
Credible intervals: “What values of θ are reasonable given the observed data x?” == P(x| θ)
Those are related as “P(θ| x) = P(θ)P(x| θ)”
Credible intervals are part of Bayesian approach.