The difference between Nom de plume and Pen name
When used as nouns, nom de plume means a pen name or pseudonym, whereas pen name means a fictitious name used by an author in place of their actual name.
check bellow for the other definitions of Nom de plume and Pen name
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Nom de plume as a noun:
A pen name or pseudonym
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Pen name as a noun:
A fictitious name used by an author in place of their actual name.