Refers specifically to the heir apparent to a throne, typically in a monarchy. Formal and official term.
The crown prince is scheduled to ascend the throne next month.
The crown prince of that country is widely beloved by the people.
王太子 is used for the crown prince of a non-imperial kingdom, whereas 皇太子 is the standard title in imperial (esp. Japanese) contexts.
crown princess
Compound of 王 (king) and 太子 (crown prince). The term is straightforward and follows standard Sino-Japanese word formation.