Aver vs. Avow: What's the Difference?

Aver and Avow Definitions
Aver
To affirm positively; declare
"Liberal politicians ... found it necessary to aver that they were in favor of rigid economy in public spending too" (John Kenneth Galbraith).
Avow
To acknowledge or declare openly and unashamedly
Avowed their faith in the electoral process.
Aver
(Law) To assert formally as a fact.
Avow
To state positively; declare
"Various church councils have avowed that evolution poses no threat to supernatural belief" (Frederick C. Crews).
Aver
(ambitransitive) To assert the truth of (something); to affirm (something) with confidence; to declare (something) in a positive manner.
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Avow
(transitive) To declare openly and boldly, as something believed to be right; to own, acknowledge or confess frankly.
Aver
To justify or prove (an allegation or plea that one has made).
Avow
(transitive) To bind or devote by a vow.
Aver
To avouch, prove, or verify the existence or happening of (something), or to offer to do so.
Avow
(legal) To acknowledge and justify, as an act done. See avowry.
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Aver
A beast of burden; chiefly a workhorse, but also a working ox or other animal.
Avow
(obsolete) avowal
Aver
An old, useless horse; a nag.
Avow
To declare openly, as something believed to be right; to own or acknowledge frankly; as, a man avows his principles or his crimes.
Which I to be the of Israel's GodAvow, and challenge Dagon to the test.
Aver
A work horse, or working ox.
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Avow
To acknowledge and justify, as an act done. See Avowry.
Aver
To assert, or prove, the truth of.
Avow
To bind, or to devote, by a vow.
Aver
To avouch or verify; to offer to verify; to prove or justify. See Averment.
Avow
Avowal.
Aver
To affirm with confidence; to declare in a positive manner, as in confidence of asserting the truth.
It is sufficient that the very fact hath its foundation in truth, as I do seriously aver is the case.
Then all averred I had killed the bird.
Avow
A vow or determination.
Aver
Report or maintain;
He alleged that he was the victim of a crime
He said it was too late to intervene in the war
The registrar says that I owe the school money
Avow
To declare or affirm solemnly and formally as true;
Before God I swear I am innocent
Aver
To declare or affirm solemnly and formally as true;
Before God I swear I am innocent
Avow
Admit openly and bluntly; make no bones about