explain vs say

explain is not a noun while say is a noun.

Word	Noun	Adjective	Verb	Adverb
explain	No	No	Yes	No
say	Yes	No	Yes	No

As verbs, say is a hypernym of explain; that is, say is a word with a broader meaning than explain:

Other hypernyms of explain include state, tell.

explain (noun)	say (noun)
	the chance to speak

explain (verb)	say (verb)
make plain and comprehensible	express in words
define	report or maintain
serve as a reason or cause or justification of	speak, pronounce, or utter in a certain way
	express a supposition
	give instructions to or direct somebody to do something with authority
	communicate or express nonverbally
	recite or repeat a fixed text
	indicate
	state as one's opinion or judgement; declare
	utter aloud
	have or contain a certain wording or form