In Europe some titles descend by primogeniture, and some titles descend to all agnatic (male line) descendants of the first title holder. And the same goes for hereditary rulers - in some principalities the rule descended to one person by primogeniture, but in other principalities the land divided among the sons of a ruler upon his death, so those principalities became smaller and smaller and more and more numerous over the years.
In the Lichtenstein dynasty, for example, the title of prince is shared by all members of the dynasty, but the rule of the principality descends to one person by agnatic primogeniture. So there are many princes of the Lichtenstein dynasty at any time but only one ruling and reigning prince of Lichtenstein at a time.
Many titles are granted so a higher title goes by primogeniture and a loer title goes to all agnatic members of the grantee's descendants. So the dynasty might have one duke and several loer ranking princes (or vice versa) or it might have one duke at a time and several counts, and so on in various other combinations.
As nearly as I can tell, it is common to describe the heir to the Duchy of X or Principality of Y as the hereditary duke of X or the Hereditary Prince of Y.
In the UK it is common for a noble to have a number of different titles. The Duke of A might be in full Duke of A, Marquess of B, Earl of C and D, Viscount of E, and Baron of F, G, H, and I, for example. So it is common to call a Duke's eldest son and heir apparent by the next senior title the Duke has - but that is just a courtesy title. So the Duke of A's heir could be called by the courtesy title of Marquess of B. And I guess the Duke's senior grandson could be called the Earl of C, and his senior great grandson could be called the Viscount of E, and his senior great great grandson could be called the Baron of F.
PS missing a letter from my keyboard.