fan letter vs letter

fan letter and letter both are nouns.

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

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

Other hypernyms of fan letter include missive.

fan letter (noun)	letter (noun)
a letter that is a piece of fan mail	a written message addressed to a person or organization
	the conventional characters of the alphabet used to represent speech
	an award earned by participation in a school sport
	a strictly literal interpretation (as distinct from the intention)
	owner who lets another person use something (housing usually) for hire

fan letter (verb)	letter (verb)
	mark letters on or mark with letters
	set down or print with letters
	win an athletic letter