A royal family is the immediate family is the immediate family of rulers of kingdoms (kings/queens, emirs/emiras, sultans/sultanas, raja/rani, etc.) and sometimes their extended family.
An imperial family describes the family of an emperor or empress.
The papal family describes the family of a pope. The baronial family describes the family of a baron. The comital family describes the family of a count/earl. The ducal family describes the family of a duke. The archducal family describes the family of a archduke. The grand ducal family describes the family of a grand duke. The princely family describes the family of a prince.