letter vs correspondence

letter and correspondence both are nouns.

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

letter (noun)	correspondence (noun)
a written message addressed to a person or organization	similarity by virtue of corresponding
the conventional characters of the alphabet used to represent speech	compatibility of observations
an award earned by participation in a school sport	(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
a strictly literal interpretation (as distinct from the intention)	communication by the exchange of letters
owner who lets another person use something (housing usually) for hire	the relation of corresponding in degree or size or amount

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