anthem vs doxology

anthem and doxology both are nouns.

Word	Noun	Adjective	Verb	Adverb
anthem	Yes	No	No	No
doxology	Yes	No	No	No

As nouns, doxology is a hyponym of anthem; that is, doxology is a word with a more specific, narrower meaning than anthem:

Other hyponyms of anthem include dithyramb, choral, chorale, canticle, hymeneal, paean, pean, recessional.

anthem (noun)	doxology (noun)
a song of praise (to God or to a saint or to a nation)	a hymn or verse in Christian liturgy glorifying God
a song of devotion or loyalty (as to a nation or school)