believer vs supporter

believer and supporter both are nouns.

Word	Noun	Adjective	Verb	Adverb
believer	Yes	No	No	No
supporter	Yes	No	No	No

As nouns, supporter is a hypernym of believer; that is, supporter is a word with a broader meaning than believer:

Other hypernyms of believer include admirer, booster, champion, friend, protagonist.

believer (noun)	supporter (noun)
a person who has religious faith	a band (usually elastic) worn around the leg to hold up a stocking (or around the arm to hold up a sleeve)
a supporter who accepts something as true	a support for the genitals worn by men engaging in strenuous exercise
	a person who backs a politician or a team etc.
	a person who contributes to the fulfillment of a need or furtherance of an effort or purpose
	someone who supports or champions something