It does include both private and public. You'd have to dig into the different reports to figure out exact methodologies (which I'm too lazy to do right now), but most reports converge on the USA being the country that spends the most on healthcare, both on a per capita basis (which is less interesting, we're richer than most other countries so we should spend more) but also on a % GDP basis. And we win by a large margin on that metric, despite getting pretty mediocre bang for buck.

Various theories explain this: inefficiencies, the USA subsidizing research for the rest of the world, etc. Really they're two sides of the same coin--those inefficiencies line the pockets of various medical-related corporations, some of which ends up going into research.