What is the difference between healthcare and medical care?

Medical care is treatment; the doctors, nurses and technicians who actually treat the patients.

"Health care" and "health coverage" generally mean "health insurance"; who PAYS for the medical care. So "health care reform" doesn't mean reforming what the doctors are doing, and "Obamacare" doesn't create doctors. They arrange for the payment of the doctors and hospitals who actually provide medical treatment.

In fact, our current systems of "health care" is causing doctors and hospitals to go out of business, because the government systems don't pay enough money for the hospitals to continue to operate. And doctors don't see patients for free.