There was much confusion all over the internet last week when the new prince's certificate of birth was publicly released because K-Middy's occupation was listed as "Princess of the United Kingdom".
Anyway, everyone was baffled etc. But guess what? Apparently you can be a princess and a duchess at the same time so it's all okay and everyone can bloomin' well calm down.
There's a rule in the British monarchy meaning a wife (in this case Kate) gets given the equivalent of her husband's rank, unless her own rank is higher.
Titles are just a matter of differentiating royals from all the other, er, royals (past and present) with the same names.
ERGO William is a prince and a duke and Kate is a princess and a duchess.