Perhaps I can offer help although I'm not Holly.
It depends a bit on circumstances, context and personal preference.
The Duke of Edinburgh is not a British Prince (he is Greek and Danish) so it is only a courtesy title in the UK.
Being Welsh I would never call Charles Prince of Wales as he is a usurper installed by the English, so I call him Prince Charles.
It is a convention to call them by their most senior title, so Philip is Duke, Charles is Prince. In strict order of precedence Philip is below Charles, and even below Princess Charlotte and Prince Louis!
Like I said, it's complicated! We have a whole College of Heralds devoted to this sort of thing!