I also found one Washington Post article from 2012 that called it the National Firearms Act of 1938:
However, every other source, including government sources, refer to it as the Federal Firearms Act of 1938.
for example, here is a Congressional Research Service report that discusses firearm laws that was written in 2019:
https://crsreports.congress.gov/product/pdf/R/R45629
A few years later, Congress enacted the Federal Firearms Act of 1938 (FFA), which created a licensing scheme for the manufacture, importation, and sale of firearms and established limited categories of persons who could not possess firearms.10 The FFA eventually was superseded, however, by the more comprehensive Gun Control Act of 1968 (GCA).11 In addition to expanding the FFAs licensing scheme and categories of prohibited personswhich largely had been restricted to certain criminalsthe GCA augmented the criminal penalties available for violations and established procedures for obtaining relief from firearm disabilities.12
Yes.
My research confirms what you found.
I issued a correction on the original article.