Most likely definitions from the context: "correct" means producing optimal outcomes, or producing beliefs most closely aligned with objective reality. "Rational" means obtained from available data using a rational process, whether or not the data is good.

So someone with bad priors can come to bad conclusions through entirely "rational" means.

Totally correct. That's why reasonable people don't agree on politics at all. Group A has one set of priors, group B has another and despite them both being basically rational, the priors lead them down totally different roads as to how to "fix things"

"Correct" ones would be those which actually maximize your outcome, while "rational" ones would be the ones are which you infer they will maximize your outcome from the information you have available.