‘Many thanks’: can it be used as a closing formula only, or is it fully synonymous with ‘Thank you very much’?

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Many thanks can be used as a closing, but it's a bit casual. For formal, use a closing like "Much appreciation" or "I appreciate..." etc.

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Thanks a lot or many thanks are similar.
Those are very acceptable in language.

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Both are very acceptable in language.
They have the same meaning
To give a grateful.

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Many thanks and thanks a lot is very acceptable.
And both are similar to give grateful.