They’re both forms of autocracy, but their ideological justification and means of maintaining control are at least somewhat different. I don’t see any particular reason why said justifications would shift from monarchical →fascist ones; if anything, I’d expect it to go in the other direction as a fascist dictator seeks to “legitimize” his rule by claiming “divine right” or naming a hereditary successor. I would be more inclined to agree with the statement “fascism is proto-monarchism.”