The Al Maktoum family calls themselves the "ruling" family not the "royal" family and most senior members of the Ruling families do not like the idea of being called royal. Maybe because royalty is a system/idea of the Western world while the UAE families are descendants of local Bedouin tribes (like the Bani Yas) and therefore they have very different mindsets and ways of governance compared to European royals.
For instance we have primogeniture or we have a rule that the first-born son must take over from the ruling monarch (King/Queen) while in the UAE or also in other Middle Eastern Ruling families (like Qatar) the Emir or the head of the family is chosing who is most suitable for taking over his position.
You may compare it to the situation in a family-run business,usually the head of the company who knows everyone and knows their ability and strengths will chose who leads the company when he/she is retired.
In traditional Royal families it is different, there is a little bit of a gamble because the firstborn or the first son is heir to the throne even if he is not the best person to fill this role.(There are different rules in different nations, most European RF allow females to inherit the Crown while in Japan only men are allowed to inherit the Chrysanthemum throne.)
To make things more complicated:In Jordan (a Royal family with Kings & Queens) they also use the tribal way of chosing a Crown Prince instead of the European first born/first son rule.
When they use the term Crown Prince for Sheikh Hamdan it is actually a little bit confusing because he will never become king. "Heir apparent" is a commonly used description for such a position which would be less misleading.
Nevertheless some young Sheikhas or Sheikhs often get called "Prince/Princess" or they sometimes even like to be addressed with that title.
Hope that my explanation helps to clear up some misunderstandings
