ACCLAMATION - noun
1 : a loud eager expression of approval, praise, or assent
2 : an overwhelming affirmative vote by cheers, shouts, or applause rather than by ballot
merriam-webster.com
# An acclamation, in its most common sense, is a form of election that does not use a ballot. "Acclamation" or "acclamatio" can also signify a kind of ritual greeting and expression of approval in certain social contexts in ancient Rome.
en.wikipedia.org/wiki/Acclamation
# Acclamation was formerly one of the methods of papal election.
en.wikipedia.org/wiki/Acclamation_(in_Papal_elections)
# A shout of approbation, favor, or assent; eager expression of approval; loud applause; The process of electing a person to a post in the absence of other nominees; : A representation, in sculpture or on medals, of people expressing joy; Without opposition in an election
en.wiktionary.org/wiki/acclamation
# acclamatory - Pertaining to, or expressing approval by, acclamation
en.wiktionary.org/wiki/acclamatory
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ACCLAIM (can be both a noun & a verb)
- transitive verb 1 : applaud, praise, 2 : to declare by acclamation
- intransitive verb : to shout praise or applause
- noun 1 : the act of acclaiming, 2 : praise, applause. eg. The book received great acclaim.
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To answer your question, what is the difference & when do we use them, I'd say, acclaim is far more commonly used than acclamation.
But if you must use acclamation, to me it sounds better in the passive tense, eg:
The acclamation received by the author was overwhelming
v
The author received overwhelming acclaim.