The difference between In a nutshell and In short
In a nutshell is also adverb with the meaning: in summary.
In short is also phrase with the meaning: as a summary.
check bellow for the other definitions of In a nutshell and In short
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In a nutshell as an adverb (idiomatic):
In summary; briefly or simply.
Examples:
"He had a lot to say, but his answer, in a nutshell, was no."