Thanks, Rosencrantz and gentle Guildenstern.

Of the two, perhaps Guildenstern is the more diplomatic, the more gentle of the gentlemen. I haven’t followed this closely through the rest of the play, but based on the evidence here, he seems to be the more graceful of the two when talking with royalty. Maybe that’s why the king gives him the “gentle” and the even more diplomatic queen smooths out the potentially ruffled Rosencrantz with her next line.
These two lines are usually played for the laugh of Rosencrantz and Guildenstern being interchangeable – that the king does not know which is which and the Queen corrects him, gently. I believe I played it that way myself – but there are other choices here – perhaps ones that go deeper than a joke at the king’s expense.