BOTH
though to be clear there are neither in Her Majesty The Prince; while there are other monarchs and nations, the one that's central to the story has only ever had princesses (and probably princes as well based on current evidence, as one of the socialites uses that term in chapter 1 without making it sound like she coined it)
(...and while it'd be a fun exercise in fantasy etymology to find a new origin for the word princess that doesn't go through making it a feminine version of prince, I think it's fair to assume both are existing concepts in the setting)

