mail vs fan mail

mail and fan mail both are nouns.

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

As nouns, fan mail is a hyponym of mail; that is, fan mail is a word with a more specific, narrower meaning than mail:

Other hyponyms of mail include hate mail, mailing.

mail (noun)	fan mail (noun)
(Middle Ages) flexible armor made of interlinked metal rings	mail sent to public figures from their admirers
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

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