fan mail vs mail

fan mail and mail both are nouns.

Word	Noun	Adjective	Verb	Adverb
fan mail	Yes	No	No	No
mail	Yes	No	Yes	No

As nouns, mail is a hypernym of fan mail; that is, mail is a word with a broader meaning than fan mail:

Other hypernyms of fan mail include post.

fan mail (noun)	mail (noun)
mail sent to public figures from their admirers	(Middle Ages) flexible armor made of interlinked metal rings
	a conveyance that transports the letters and packages that are conveyed by the postal system
	the system whereby messages are transmitted via the post office
	the bags of letters and packages that are transported by the postal service
	any particular collection of letters or packages that is delivered

fan mail (verb)	mail (verb)
	cause to be directed or transmitted to another place
	send via the postal service