From my perspective (linguistic anthropology), they’re not actually all that close. Most historical “queens” (which have that label applied to them by modern English speakers) were not rulers (and we have a separate term, “queen regnant”, for that) but rather the gender dual to the male “royal consort.” It was only in recent history where you see examples of “equal-opportunity” monarchies that could have either a male or female monarch of equal power, and thus usages of “queen” to denote those monarchs.

Thus—given that we’re defining words based on their centroids of usage in a historical corpus—if a woman is a monarch of a kingdom, “king” is a tighter historical fit to describe her role than “queen” is.