house of God vs house of prayer

house of God and house of prayer both are nouns.

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

As nouns, house of God and house of prayer are synonyms defined as:

house of God and house of prayer: any building where congregations gather for prayer

Other synonyms of house of God include house of worship, place of worship.

house of God (noun)	house of prayer (noun)
any building where congregations gather for prayer	any building where congregations gather for prayer