varsity letter vs award

varsity letter and award both are nouns.

Word	Noun	Adjective	Verb	Adverb
varsity letter	Yes	No	No	No
award	Yes	No	Yes	No

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

Other hypernyms of varsity letter include accolade, honor, honour, laurels.

varsity letter (noun)	award (noun)
an award earned by participation in a school sport	a grant made by a law court
	a tangible symbol signifying approval or distinction
	something given for victory or superiority in a contest or competition or for winning a lottery

varsity letter (verb)	award (verb)
	give, especially as an honor or reward
	give as judged due or on the basis of merit