King of the Hellenes means "King of the Greeks", whereas, the king's children would be just prince(ess) of the country, Greece (and of course Denmark). Although, I don't know if this same rule applies for another countries with a constitutional monarchy.
Would it be--
Queen of the British or just UK?
King of the Norwegians/Swedes/Danes? (I know they're not the same country anymore, but you get the idea).
And was Kaiser Wilhelm II Emperor of the Germans or just 'of Germany'?