No forget insurance altogether. Socialized health care is absolutely not a form of insurance. That's not what any of those words mean.

You might be thinking of single payer healthcare but that's not what I'm arguing for. It feels like you've got a very high school level understanding of words and are trying to discuss concepts without understanding the distinction and mashing things together. Just because things might have a few overlapping points doesn't make them the same thing. That's not how language works.

A government run system, of which only two exist that I know of, the NHS and IHS (Indian healthcare system for native Americans), are not insurance. They aren't a pooling of risk, they're a taxpayer paid service. It's a complete flip from what insurance is. Just because they have to pool taxpayer money to fund it does not make it insurance.