First of all, the FDA itself has no so-called certification, just for our convenience. Since there is no certification, there is no certificate, so the so-called certificates issued by many service organizations are actually useless.
The FDA can be called registration, and the registration should determine the process and documents to be submitted according to the specific products. For example, some medical devices need to apply for the code of 5 10K first. To apply for this code, you need to provide relevant documents to prove that a product meets the safety characteristics of products already on the market. How to prove that it involves relevant standards and standards-based testing, which is what you call FDA testing.
This test does not specify which institution to do it, and it is a kind of self-guarantee. However, the testing of medical equipment can only be done by those institutions.
In addition, there are other types of products FDA testing, such as food contact materials, cosmetics, etc., which are carried out in accordance with the laws and regulations stipulated by the FDA.