Socialized healthcare: The government hires the doctors and nurses, build the hospitals, every citizen has free (paid in the form of taxes of every citizen not per-visit individual paid) healthcare.
Universal coverage: Doctors and nurses work for private companies, private companies build the hospitals, every citizen has free (paid by taxes) healthcare.
Private coverage: Doctors and nurses work for private companies, one can only afford to go to the doctor by paying for insurance.
What's being proposed in a nutshell is expanding private coverage by using private insurance companies to cover almost all citizens. That's about as far from “government run healthcare” and as weak as “reform” can get and still be called reform. Yet, the GOP is still pretending that they are the only thing standing between a hardworking individual and a socialist nightmare being rammed down America's throat in the dead of night with backroom deals and sweetheart deals that aren't on C-SPAN. In reality the GOP is standing between sick people and doctors while warning of “government bureaucrats standing in between you and your doctor”.
Providing an insurance pool run by the government such as the “public option” open to any citizen was criticized as being too radical of an idea by the GOP, and they managed to quash it. In all fairness though it is a radical idea to anyone from 1910, or anyone that's never had to choose between a mortgage or medicine.