admirer vs supporter

admirer and supporter both are nouns.

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

As nouns, admirer and supporter are synonyms defined as:

Other synonyms of admirer include booster, champion, friend, protagonist.

admirer (noun)	supporter (noun)
someone who admires a young woman	a band (usually elastic) worn around the leg to hold up a stocking (or around the arm to hold up a sleeve)
a person who backs a politician or a team etc.	a support for the genitals worn by men engaging in strenuous exercise
a person who admires; someone who esteems or respects or approves	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