idolater vs idol worshiper

idolater and idol worshiper both are nouns.

Word	Noun	Adjective	Verb	Adverb
idolater	Yes	No	No	No
idol worshiper	Yes	No	No	No

As nouns, idolater and idol worshiper are synonyms defined as:

Other synonyms of idolater include idoliser, idolizer.

idolater (noun)	idol worshiper (noun)
a person who worships idols	a person who worships idols