Is patented health food under the management of the State Food and Drug Administration?

the patent belongs to China National Intellectual Property Administration; Health products are under the control of the Food and Drug Administration. The products you mentioned are managed by both departments. The difference is:

China National Intellectual Property Administration has granted you a patent right, and you can legally prohibit others from implementing it for the purpose of production and operation.

It has been approved by the State Food and Drug Administration, and you can produce and implement it yourself. (The Food and Drug Administration does not approve it, and you are not allowed to produce it if you have a patent).