HRH is a special status (in the ruling Monarchies only) granted by the ruling monarch. The status comes with certain privileges and duties on behalf of the state, paid for by the state (the people).
In the recent case in Sweeden, some members of the Royal Family have been stripped off of their HRH status not to be confused with a prefix title. There are cases in the UK as well. For example, Sarah Ferguson, The Duchess of York who previously held the HRH status and was then known as HRH Sarah, The Duchess of York, that status came with privileges and duties on behalf of the ruling monarch as well as Diana Spencer, Princess of Wales who held titles of HRH Diana, The Princess of Wales and Duchess of Rothesay.
Now, prefix titles or otherwise known as courtesy titles are similar to Mr/Mrs, Miss/Ms, His/Her Grace, The Hon, The Right Hon, Sir, Lady, His/Her Holiness, His/Her Excellency, and alike. Prefix titles of HRH are applied to the members of the Royal Family that are no longer in power of the state business (non-ruling Monarchies) and ruling Monarchies address them simply as Prince/Princess X, Duke/Duchess X, Count/Countess X but not HRH The Prince/Princess X, HRH The Duke/Duchess X, HRH The Count/Countess X, however, they do use verbal form of courtesy titles and do address them as Your Highness, Your Serene Highness, Your Imperial Highness sometimes even Your Royal Highness (even though they are no longer in power).
I agree with Elaine that HRH is not relevant to genealogy either as a status title or prefix title. I went through many genealogical papers and books and I haven't seen HRH in them at all, just the titles, eg Name, King X or Name, The Duke of X. However, I did see courtesy titles in many aristocratic genealogical papers and books with genealogical tables in them which can be useful as a piece of additional information in the bio section to list their full name and title for example name on the page: Bernard Montgomery
Viscount Montgomery of Alamein and in the bio section: Field Marshal Bernard Law Montgomery, 1st Viscount Montgomery of Alamein, KG, GCB, DSO, PC, DL.
I hope this is helpful.
