equal vs correspond

equal is a noun but correspond is not a noun.

Word	Noun	Adjective	Verb	Adverb
equal	Yes	Yes	Yes	No
correspond	No	No	Yes	No

As verbs, correspond is a hyponym of equal; that is, correspond is a word with a more specific, narrower meaning than equal:

Other hyponyms of equal include equate, agree, check, fit, gibe, jibe, match, tally, represent, stand for, translate.

equal (noun)	correspond (noun)
a person who is of equal standing with another in a group

equal (adjective)	correspond (adjective)
having the same quantity, value, or measure as another
having the requisite qualities or resources to meet a task

equal (verb)	correspond (verb)
make equal, uniform, corresponding, or matching	exchange messages
be identical or equivalent to	be compatible, similar or consistent; coincide in their characteristics
be equal to in quality or ability	take the place of or be parallel or equivalent to
	be equivalent or parallel, in mathematics