sympathizer vs friend

sympathizer and friend both are nouns.

Word	Noun	Adjective	Verb	Adverb
sympathizer	Yes	No	No	No
friend	Yes	No	No	No

As nouns, friend is a hypernym of sympathizer; that is, friend is a word with a broader meaning than sympathizer:

sympathizer: someone who shares your feelings or opinions and hopes that you will be successful
friend: a person who backs a politician or a team etc.

Other hypernyms of sympathizer include admirer, booster, champion, protagonist, supporter.

sympathizer (noun)	friend (noun)
someone who shares your feelings or opinions and hopes that you will be successful	a person you know well and regard with affection and trust
a person who commiserates with someone who has had misfortune	a person with whom you are acquainted
	an associate who provides cooperation or assistance
	a person who backs a politician or a team etc.