I'm not sure how Wikipedia is distinguishing them but for the most part firearms do not have to be registered in the United States. Some states require firearms to be registered but most do not. Unregistered firearms can nonetheless be counted because they are inventoried and sold legally (firearms dealers must be licensed and regulated), even though the end purchaser is not registered anywhere.

Federally, only specific categories like fully-automatic machine guns and short-barreled rifles have to be registered.