Why not just remain “Prince of Wales” the whole time?
So the prince of wales is a title given to the heir to the British throne. He has only become prince of wales now that his father is the reigning monarch.
Duke of Cambridge was a title bestowed on him by the queen as a wedding present.
While Wales was the family name both William and Harry used when needed, for example during their military service, Prince William has never been titles the Prince of Wales before now.
Given that he was the son of the prince and princess of Wales though, the confusion is very understandable.
Edit: regarding using Wales as a family name, his last name is actually Windsor, Wales is just kind of a lazy alias.
The now King Charles was *The* Prince of Wales: that was one of his titles. As children of Charles, both William and Harry were Princes, and could use the styling ‘Prince William/Harry of Wales’, but were not themselves the Prince of Wales.
On his marriage, Prince William was created as Duke of Cambridge by the late queen, and it became an additional title for him. As he was the only person entitled to refer to themselves as Duke of Cambridge, this became his primary royal styling.
Once his father acceded the crown as King Charles III, William was created as *The* Prince of Wales, as his father had vacated that office.
William wasn’t Prince of Wales as a child; that was his dad.
When he married, his grandma gave him Cambridge as a wedding gift (well, the title Duke of Cambridge anyway).
Once Charles became King, the title of Prince of Wales became vacant and the King awarded it to William.
I’m not sure if the eldest son of the monarch usually gets that title or if it’s more of a coincidence that the two of them have both held the title.
He was born *to* the Prince of Wales (Charles). As such, he was styled Prince William of Wales, and his brother Prince Harry of Wales. So, he was not the Prince of Wales. That’s reserved for the first in line to the throne.
When British princes get married, they’re usually gifted a title from the sovereign. Prince William received the Duke of Cambridge and was known as that.
When the Queen died, William’s father became King. The title of the Prince of Wales was then given to William. As he is now the first in line to throne. His children used to be “of Cambridge”. Now they are “of Wales”.