synagogue vs house of worship

synagogue and house of worship both are nouns.

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

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

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

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