correspondence vs agreement

correspondence and agreement both are nouns.

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

As nouns, correspondence and agreement are synonyms defined as:

correspondence (noun)	agreement (noun)
similarity by virtue of corresponding	compatibility of observations
compatibility of observations	the thing arranged or agreed to
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane	the verbal act of agreeing
communication by the exchange of letters	the statement (oral or written) of an exchange of promises
the relation of corresponding in degree or size or amount	the determination of grammatical inflection on the basis of word relations
	harmony of people's opinions or actions or characters