The difference between Pen-name and Pseudonym
When used as nouns, pen-name means a writer's pseudonym, whereas pseudonym means a fictitious name, as those used by writers and movie stars.
check bellow for the other definitions of Pen-name and Pseudonym
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Pen-name as a noun:
A writer's pseudonym
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Pseudonym as a noun:
A fictitious name, as those used by writers and movie stars.
Examples:
"The Reverend Charles Lutwidge Dodgson wrote "Alice's Adventures in Wonderland" under the pseudonym Lewis Carroll."