synagogue vs house of prayer

synagogue and house of prayer both are nouns.

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

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

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

synagogue (noun)	house of prayer (noun)
(Judaism) the place of worship for a Jewish congregation	any building where congregations gather for prayer