idolater vs idolizer

idolater and idolizer both are nouns.

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

As nouns, idolater and idolizer are synonyms defined as:

Other synonyms of idolater include idol worshiper, idoliser.

idolater (noun)	idolizer (noun)
a person who worships idols	a person who worships idols
	a lover blind with admiration and devotion