No such thing as a specific gunsmith license. There is no recognized government standards other than the definitions provided in the Code of Federal Regulations. No bar exam, board of review, competency tests. If you modify guns for your occupation you are a gunsmith. If you do it on the side or for fun then you are not. There are "certifications" that you can earn from learning institutions but holding one is not a requirement for licensing. A recognized certification and valid FFL license together will allow you to purchase certain restricted parts. Usually trigger stuff and the recognition of said certifications varies by each vender.
The definition of a gunsmith is you must be Engaged in the business.
as defined in the Code of Federal Regulations - Title 27: Alcohol, Tobacco Products and Firearms
[27 CFR 478.11 meaning of terms]
Engaged in the business is defined as:
(d) Gunsmith. A person who devotes time, attention, and labor to engaging in such activity as a regular course of trade or business with the principal objective of livelihood and profit, but such a term shall not include a person who makes occasional repairs of firearms or who occasionally fits special barrels, stocks, or trigger mechanisms to firearms
The 01 FFL is the only license you need. It in itself requires you to comply with all local regulations to practice the occupation of gunsmith.