Royal address is no different from any other form of address; the correct usage is dependent on local etiquette and custom and the relationship between the parties. For example, Catholic bishops in the United States are customarily addressed orally as Your Excellency, whereas Catholic bishops in Ireland are customarily addressed orally as Your Grace. But it's entirely possible that Cardinals O'Malley and Wuerl, meeting casually for coffee, would address each other as Patty and Don (I don't know if they would, but there's certainly no "rule" of "English" against it).
There are too many of these rules to explain here; entire books are published as guides to correct forms of address. Moreover each realm may have specific customs related to styles and address— for example, Canada and Australia have slight differences in their official royal style and titles, even though the same person is monarch of both.
As a matter of practice, the British royal family— the de facto royal family in the English-speaking world, even in republics— actually has a guide to greeting a member of the royal family, which opens with the note
There are no obligatory codes of behaviour when meeting The Queen or a member of the Royal Family, but many people wish to observe the traditional forms.
These latter include a bow or a curtsy, then
On presentation to The Queen, the correct formal address is 'Your Majesty' and subsequently 'Ma'am,' pronounced with a short 'a,' as in 'jam'.
For male members of the Royal Family the same rules apply, with the title used in the first instance being 'Your Royal Highness' and subsequently 'Sir'.
For other female members of the Royal Family the first address is conventionally 'Your Royal Highness' and subsequently 'Ma'am'.