Captain Cook's exploration ship began as a collier

What class was Captain Cook's ship?

It was a converted collier, a merchant ship or bark rather than a purpose-built warship.

Captain Cook's vessel was a converted collier, described here as a merchant ship or bark. Its construction background places it outside the naval combat ratings. The hull began in commercial service and was adapted for exploration instead of being built as a warship. The short answer shows how an exploration vessel could acquire a new role without losing the practical character of its original design.