Oh, also the USA is, by practical definition, purely free market.
I say practical because there aren't any industries where the government owns the means of production unless you count interplanetary space probes, or military operations.
I also want to say manned space flight, but the private sector has recently entered that industry (though you may include it as the private sector doesn't technically do it on a commercial basis yet.) The private industry manufactures military equipment though (e.g. fighter jets are made by Boeing and others and purchased by the government.)
Most western countries have some kind of socialized medicine (i.e. in Canada, all medical personnel work for the government and are forbidden from running a private practice, whereas in the UK private practice is permitted but it's mostly only for rich people who can afford people who they believe do a better job than the NHS workers.)
However the US does not. In the US, "government paid" medicine comes in the form of an HMO type insurance that just pays all of your medical expenses to private companies, and then charges you almost nothing for it; but the private sector still owns the means of production. It only truly fits the definition of welfare and not socialism.
When the ultra conservatives say the US has the best medicine though, I'm inclined to agree. If you look at countries with socialized medicine, virtually all of them have contracts arranged with private hospitals in the US where they send their people if their country doesn't have the facilities available.
Usually this is something super specialized. For example, their worst cancer patients that have a chance of recovery are sent to MD Anderson Cancer Center in Texas. Other fields such as Neurosurgery, Pulmonology, Cardiology, and other specialties for vital organs are often sent to Mayo Clinic or Johns Hopkins centers. Countries I know of who have sent their patients here for these include Canda, UK, Germany, and Sweden.
Where the US tends to look bad in the rankings are individual hospitals that mainly just serve ER patients who don't bother shopping around, so their service can suck but they can still bill stupidly high amounts. Because there are so many of these hospitals, it makes the average US hospital look less than stellar.
That said, knowing what I know about how socialism impacts other industries, I think it would be a mistake for the US to switch to socialized medicine. We do spend too much on medicine however. I think one way to fix that might be to add a bit of regulation stipulating that doctors and hospitals be required to show their rates for the most common services that they provide up front, and before you are provided any services, you as a patient are given the right to know what your bill will be BEFORE the service is performed if you just ask.
This would end hospital/ER sticker shock and billing errors (which are at something like 90%) and at the same time force medical staff to be more competitive on price. Even if you're insured, it would be preferable to shop around since most people have a deductible to deal with.
Also, in my opinion, the Affordable Care Act is only going to raise prices, and they're already high enough, because all it does is raise the demand for medical services without doing anything to address how much is paid out to those services.