What is the relationship between the Health and Health Commission and the Health Bureau?

It doesn't matter. These are two independent departments. The difference between the Health Bureau and the Health and Health Commission lies in their different powers. As a component of the State Council, the Health and Wellness Committee is responsible for formulating national health and wellness policies and plans, coordinating and deepening the reform of the medical and health system, implementing disease prevention and control plans, and managing state administration of traditional chinese medicine. Moreover, the Health Bureau is a subordinate unit of the local government, at the county level, responsible for the treatment of infectious diseases and chronic non-communicable diseases, as well as the development planning of local Chinese medicine work to promote the development of integrated traditional Chinese and western medicine, so it has nothing to do with it, and it is two independent departments.