anthem vs song

anthem and song both are nouns.

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

As nouns, song is a hypernym of anthem; that is, song is a word with a broader meaning than anthem:

Other hypernyms of anthem include vocal.

anthem (noun)	song (noun)
a song of praise (to God or to a saint or to a nation)	the act of singing
a song of devotion or loyalty (as to a nation or school)	a short musical composition with words
	the characteristic sound produced by a bird
	a distinctive or characteristic sound
	a very small sum