meetinghouse vs house of prayer

meetinghouse and house of prayer both are nouns.

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

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

meetinghouse: a building for religious assembly (especially Nonconformists, e.g., Quakers)
house of prayer: any building where congregations gather for prayer

Other hypernyms of meetinghouse include house of God, house of worship, place of worship.

meetinghouse (noun)	house of prayer (noun)
a building for religious assembly (especially Nonconformists, e.g., Quakers)	any building where congregations gather for prayer