agreement vs correspondence

agreement and correspondence both are nouns.

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

As nouns, agreement and correspondence are synonyms defined as:

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