say vs aver

say is a noun but aver is not a noun.

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

As verbs, say and aver are synonyms defined as:

Other synonyms of say include allege.

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

say (verb)	aver (verb)
express in words	to declare or affirm solemnly and formally as true
report or maintain	report or maintain
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