The Royal Forums has a whole thread devoted to explaining titles and how they work, as well as how they are acquired. (And several threads devoted to historical titles and how those people acquired them.)
Titles are hierarchical. You have them but you don't use them until you move up the ladder. Catherine goes by Duchess of Cambridge because the the next up on the ladder is Camilla. Camilla, by choice--out of respect for the late Diana--chooses to use Duchess of Cornwall, but she is technically the Princess of Wales. Kate has the title Princess of Wales, but she's 2 removed from throne, so she uses her second most important title. But Kate is still Princess Catherine even though she's referred to as the Duchess of Cambridge. (Even though she's technically Catherine, Princess of Wales, everybody shorthands it because it's easier. After Diana lost her HRH title, she was still referred to as Princess Diana, even though it wasn't technically correct to do so. And, yes, Grace was called Princess Rainier. But people aren't educated about how titles work or the protocol on how to use/title people. Which is why the Palace is shorthanding the information. Charlene is Princess Albert, and Charlene, Princess of Monaco.)
To put it another way: Prince William is still the Prince of Wales, even though he goes by the Duke of Cambridge. However, since he's 2 removed from the throne, he doesn't go by Prince of Wales, he goes by his second most important title: DoC. (He has several lesser titles as well.)
I'll find and link the titles here. It's very informative and educational.
