FDA is Initials of Food and Drug Administration in America.
There is a difference between FDA Approved and FDA Compliant. No materials are FDA Approved, but may be FDA Compliant. The US FDA does not test material, rather it sets standards against which materials may be tested by the supplier for compliance to a set of standards. This is true for carbon black and in FDA 21CFR 178.3297 there are detailed standards. And this request is for food indirect contact, no carbon black could be suggested to put into what we eat.
The testing is very thorough and includes maximum levels for residual levels of many things in the material. For carbon black, such things as Lead, Volatile Organic Compounds (VOC's) and Poly Aromatic Hydrocarbons (PAH's) are tested and reported. If the contents of the material do not exceed the maximum allowable levels in the FDA regulation, the material is considered to be FDA Compliant.
Channel Black is considered FDA Compliant due to the production process, and is sold as FDA Compliant because the production process was deemed to be compliant. In years past, when Channel Black was produced by the original process - impinging a gas flame onto a steel channel and scraping off the carbon black - the process did indeed produce a material that met the FDA Compliance regulation when tested. Today, the producers of Channel Black use an oil flame which in all test results that I have seen leaves high levels of impurities such as PAH's in the product making them not meet the regulation. However, the Channel Black process is still in the US law and FDA regulation as compliant so producers and consumers go by this rule.
The furnace process is capable of producing FDA Compliant grades. There are FDA Compliant grades produced by the furnace process which both Cabot and Orion make and market in the US. The testing shows that the material does not exceed the regulation. Therefore, these products comply with the regulation and are sold as such.