Very often, a member of the peerage of the UK will have subsidiary titles of lesser rank. For example, a duke may also hold an earldom and a barony. When this happens, the oldest (surviving) son of the peer may use a subsidiary title. For example, Prince Edward is the Earl of Wessex. He also has a subsidiary title, Viscount Severn, which is used by his son.
If the peer has two subsidiary titles, the oldest son of his oldest son may use the secondary subsidiary title. For example, David Somerset is the Duke of Beaufort. His son, Henry, uses the courtesy title of Marquess of Worcester, a title rightfully belonging to his father. Henry’s son, Robert, uses the courtesy title Earl of Glamorgan (Earl ranking lower than a Duke or a Marquess).
Prince Phillip (the Queen’s husband) is the Duke of Edinburgh. He also holds the subsidiary titles of Earl of Merioneth and Baron Greenwich.
Prince Charles, it is assumed, is entitled to use the title Earl of Merioneth. However, since he is (in his own right) the Duke of Rothesay and the Duke of Cornwall (and the Prince of Wales), he would not use the courtesy title of an Earl.
However, William (before his creation as Duke of Cambridge) is the grandson of Prince Phillip and, I would imagine, should have been entitled to use Baron Greenwich as a courtesy title. Why did he not use the title? In addition, I suppose it could also be asked why Charles was not styled as Earl of Merionth before his mother’s ascension?