Medicaid is Medicare for the poorest Americans and is part of Medicare. Medicare does not directly employ medical doctors but it too is a managed care system staffed by qualified medical professionals who run the precertification process.No, Medicare is not socialized medicine. Socialized medicine is when the government pays for health care and operates the hospitals. In Medicare, the government pays for doctors and hospitals, but does not own or employ them.
Medicare is a publicly funded health care program that ensures a universal right to health care for people age 65 and older. It was enacted in 1965 through the Social Security Act.
Medicare is not the only example of publicly funded health care in the United States. Other examples include: Medicaid, Veteran's Affairs.
The Veterans Administration (VA) system is an example of socialized medicine in the United States.
https://en.wikipedia.org/wiki/Socialized_medicine#:~:text=Medicare and Medicaid are forms,the senior, not the government.
As for your attempt to distinguish socialized healthcare from Medicare consider this. During COVID the healthcare system in my area which is a system of licensed nonprofit hospitals which like all nonprofit hospitals turn profits but are not taxed had some anti mask employees who refused to mask up.
In response the president of the system took the employees out and showed them what the bear did in the woods by informing them of the fact that 66% of the healthcare system's revenues comes directly from Medicare and if the system wanted to continue to do business with Medicare those people would either mask up or get out.
What Medicare wants Medicare gets and whether or not it's considered socialized medicine it is however the system's lowest cost provider because it has no shareholder pockets to line and it's system of fee negotiation has brought some degree of price controls to the industry.