Is there any connection between them in terms of health insurance?
Former Labor Bureau, former Personnel Bureau.
Now merged, collectively known as: Human Resources and Social Security Bureau.
The Social Security Fund Management Bureau you mentioned should be called: Social Insurance Management Bureau.
The Social Security Bureau is responsible for five major types of insurance: work-related injury insurance, maternity insurance, pension insurance, unemployment insurance, and medical care.
The Medical Insurance Management Center and the Social Insurance Administration Bureau are subordinate to the Human Resources and Social Security Bureau and have a superior-subordinate relationship.
The Social Insurance Administration Bureau is called the Director, and the Medical Insurance Management Center is called the Director, but they are generally team members of the Human Resources and Social Security Bureaus.