One of the primary things that shows a member of the Royal Family’s status is their title and style. The title is the part which precedes their name and the style is what determines how one addresses the royal. Royal titles haven’t always been as they are now. The title of Prince/Princess has meant different things over the years too!
It was during George I’s reign that the title of Prince began to mean something again. Before, the title was handed to many different people, included non-relations of the Royal Family. George I instituted calling his sons Princes with the style of Royal Highness, whilst grandchildren were princes with the style of just Highness. Royal Highness ranks higher than just Highness.
The style of HRH (Royal Highness) means His/Her Royal Highness and is prefixed to many Royal Titles, not just Prince/Princess. Control over the use of HRH and Prince/Princess was still, despite George I’s changes, rather relaxed and by the 20th century all kinds of relations of the Monarch were ‘entitled’ to the style of Prince/Princess.
It wasn’t until during WW1 that the then King, George V realised that such allowances for British titles could spell disaster for him and his family, he was essentially a German Monarch in Britain. In order to keep confidence with the British People and to not seem to be siding with the Germans, he restricted the right to the title of Prince/Princess in a special order in 1917, removing the right for his German relatives to bear the title.
This was known as the 1917 Letters Patent and is one of the most quoted letters patent by royal commentators. The exact order of the letters patent exclusively reserved the right of the title of Prince/Princess and the style of Royal Highness to ‘all children of the sovereign, all male-line grandchildren of the sovereign (children born to sons of the Monarch) and the son of the son of the Prince Of Wales.’
In order to ensure the first born child of the Duke and Duchess of Cambridge was definitely a Prince/Princess, a special order by Her Majesty The Queen was instituted 2013 Letters Patent, granting the style of Royal Highness and Prince/Princess to all children of Prince William, regardless of gender. Had this not have happened, under the 1917 letters patent, a first son would be a Prince, but any other children would be Lords and Ladies.
Nowadays, the style of just Highness (His/Her Highness) is never used in the British Monarchy, instead, the style of Royal Highness is the only style used for descendants of the Monarch.
It is possible to hold the style of Royal Highness without being a Prince or Princess. Dukes, Duchesses, Earls, Countesses and more have all been given the style of HRH in the past without becoming Princes. A notable example of this would be when The Duke Of Edinburgh (then Philip Mountbatten) became engaged to the then Princess Elizabeth (now Queen Elizabeth II) in 1947. The King [George VI] granted the title of Duke Of Edinburgh and the style of Royal Highness to Philip who still bears the title to this day. He was made a Prince by Queen Elizabeth in 1956.
Equally, though there are no modern day examples, the title of Prince/Princess could also be held without the style of Royal Highness. The two are separable.
Wives of Princes and those with the style of Royal Highness can assume the female form of their husband’s title. That’s why the Duchess of Cambridge is officially, Her Royal Highness Princess William, Duchess Of Cambridge, where Prince William is His Royal Highness Prince William, Duke Of Cambridge and the Duchess of Sussex, likewise, bears the title Her Royal Highness Princess Henry. Hence, the correct representation on the birth certificates of their respective children which records both Kate and Meghan as ”Princess of the United Kingdom” in the box noting mother’s rank, trade or occupation.
There have also been instances where those entitled to the style of Royal Highness and title of Prince/Princess have been denied their title by special orders from Her Majesty. Prince Edward’s children, under the 1917 letters patent, should be styled as ‘His Royal Highness Prince James of Wessex’ and ‘Her Royal Highness Princess Louise of Wessex’, though in an attempt to remove some of the burdens associated with royal titles, Prince Edward and The Queen agreed that his children would be styled as children of an Earl.
Some people argue that this doesn’t carry enough force to override the 1917 letters patent and that Edward’s children are still Princes and Princesses. They are styled as James, Viscount Severn and The Lady Louise Windsor. There’s nothing stopping The Queen revoking this at a later time and allowing Prince Edward’s children to be princes and princesses. And as has been discussed a lot recently, as things stand when the Prince of Wales succeeds as king then his fourth grandchild will automatically become Prince Archie according to those letters patent.