The law in question is ITAR (International Traffic in Arms Regulation). ITAR requires anyone who manufactures OR exports controlled items to register, follow a set of procedures to avoid improper export of things or information, and to pay an annual $2,250 fee.
The manufacture of some firearms does not require ITAR registration and compliance. For example, O/U shotguns suitable only for sport. Other things besides firearms are also covered by ITAR. For example, manufacture of certain firearm parts (which don't require the manufacturer to have a Federal Firearms License), military-grade scopes, or encryption software.
ITAR compliance is more than just paying a fee, it is complying with a set of procedures. For example, even it you don't send a covered item outside the USA, it is still an "export" under the law to give the item to an non-US citizen, even if they are here in the US. It is also an "export" of controlled technology to send outside the US or give a non-US citizen certain information (like manufacturing specs) about controlled products.
ITAR is enforced by the Directorate of Defense Trade Controls (DDTC), an agency in the State Department. They have previously advised that certain activities that the ATF considers "manufacturing," and which require a manufacturing FFL, do not require ITAR registration. For example, assembly of complete firearms from parts made by others for commercial sale. ATF considers that "manufacturing" (and requires a Type 07 FFL), DDTC does not. There are other activities the ATF considers "gunsmithing" (and not manufacturing), like drilling a receiver to attach a scope mount or threading a barrel. A gunsmith requires a Type 01 FFL (dealer), not a manufacturing FFL. The DDTC, however, recently published an interpretation of ITAR that makes any modification that includes cutting or drilling to improve a firearm to be "manufacturing" under their definition--which means the gunsmith would have to register and pay the ITAR annual fee.
Many in the US House and Senate are fighting this interpretation.