Lets get down to practical definitions:
Medical Insurance. That’s when a company engages in a contract with an individual or group with the cost determined by the health risk and coverage limits. Government health plans are not insurance contracts.
Government health “insurance”. That’s simply a tax payer socialized health care plan. The individual pays some or none of the expense and the government pays the rest. Medicare, Medicare, VA.
Medical care. That’s simply the provision of medical services. It can be paid by the individual, private insurance or combination of the above.
Health care. That’s when someone engages in efforts to maintain their health which sometimes includes medical care. This primarily involves nutrition, exercise, life style. Some people like to conflate health care with medical care in order to confuse the issue.
If we can use these clear definitions, we can avoid being confused by policy-makers that intentionally seek to confuse the public (remember Gruber).
Only one quibble, the government doesn't pay for anything, they get their funding thru taxes, so it's basically redistribution/transfer from those who don't use it to those who do and those who abuse it.