I assumed Crown Princess (or Prince) was merely a title given, a fancier twist, if you will. But once I thought about it, I remembered that with royals, nothing is happenstance or done on a whim. So I looked further into the title of ‘Crown Princess.’
A ‘Crown Princess’ is heiress apparent.
The perfect example is the Swedish Royal Family:
The first born of King Carl XVI Gustaf and Queen Silvia of Sweden is Victoria. Since she will then inherit the throne (thanks to the 1979 Act of Succession), she is Crown Princess Victoria.
The King’s two other children are then simply Prince Carl Philip, and Princess Madeleine.