pagan vs idolater

pagan and idolater both are nouns.

Word	Noun	Adjective	Verb	Adverb
pagan	Yes	Yes	No	No
idolater	Yes	No	No	No

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

Other hyponyms of pagan include paynim, idol worshiper, idoliser, idolizer.

pagan (noun)	idolater (noun)
a person who does not acknowledge your god	a person who worships idols
a person who follows a polytheistic or pre-Christian religion (not a Christian or Muslim or Jew)
someone motivated by desires for sensual pleasures

pagan (adjective)	idolater (adjective)
not acknowledging the God of Christianity and Judaism and Islam