Hillary is now denying that she has ever advocated socialized medicine.
It depends on what you mean by "socialized," I suppose. She didn't advocate a single, government-owned enterprise for which all doctors would work. She pushed a system where there were local HMO monopolies - kind of like local phone companies - heavily regulated but privately held.
Is there a difference? Probably some. But as the level of regulation increases, the differences start to disappear. What does it mean to have a "private company" if government regulations completely determine the company's course of action?
Ownership without control
Is just a body without a soul.