antipope vs Bishop of Rome

antipope and Bishop of Rome both are nouns.

Word	Noun	Adjective	Verb	Adverb
antipope	Yes	No	No	No
Bishop of Rome	Yes	No	No	No

As nouns, Bishop of Rome is a hypernym of antipope; that is, Bishop of Rome is a word with a broader meaning than antipope:

antipope: someone who is elected pope in opposition to another person who is held to be canonically elected
Bishop of Rome: the head of the Roman Catholic Church

Other hypernyms of antipope include Catholic Pope, Holy Father, pontiff, pope, Roman Catholic Pope, Vicar of Christ.

antipope (noun)	Bishop of Rome (noun)
someone who is elected pope in opposition to another person who is held to be canonically elected	the head of the Roman Catholic Church