house of prayer vs edifice

house of prayer and edifice both are nouns.

Word	Noun	Adjective	Verb	Adverb
house of prayer	Yes	No	No	No
edifice	Yes	No	No	No

As nouns, edifice is a hypernym of house of prayer; that is, edifice is a word with a broader meaning than house of prayer:

house of prayer: any building where congregations gather for prayer
edifice: a structure that has a roof and walls and stands more or less permanently in one place

Other hypernyms of house of prayer include building.

house of prayer (noun)	edifice (noun)
any building where congregations gather for prayer	a structure that has a roof and walls and stands more or less permanently in one place