house of prayer vs house of God

house of prayer and house of God both are nouns.

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

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

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

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

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