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.
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