Let's talk about Meghan's new title, shall we? #RoyalWedding
Today, the Queen gave Harry a title upgrade. The "promotion" means that he isn't known as HRH Prince Henry/Harry of Wales anymore (though people will still call him that). He is now known simply as HRH The Duke of Sussex, because British royals always use their highest title.
Meghan is now a princess, because she just married a prince (note the lowercase "p" in both cases). Because British royal women take their husband's rank and title, she is now a princess (rank) who is called HRH The Duchess of Sussex (title).