That's not correct, while manfacturers/importers don't have to make serial numbers unique from other manufacturers/importers, after 1968 they cannot duplicate serial numbers within their own products.
https://www.ecfr.gov/cgi-bin/text-id...e27.3.479_1102
"The serial number must be placed in a manner not susceptible of being readily obliterated, altered, or removed, and must not duplicate any serial number placed by you on any other firearm."
So serial numbers are unique within the products manufactured/imported by a particular licensee, even if different types, models, and/or calibers, but may be the same serial number used by a different manufacturer/importer.