ministry vs priesthood

ministry and priesthood both are nouns.

Word	Noun	Adjective	Verb	Adverb
ministry	Yes	No	No	No
priesthood	Yes	No	No	No

As nouns, priesthood is a hypernym of ministry; that is, priesthood is a word with a broader meaning than ministry:

ministry (noun)	priesthood (noun)
the work of a minister of religion	the body of ordained religious practitioners
building where the business of a government ministry is transacted
a government department under the direction of a minister of state
religious ministers collectively (especially Presbyterian)