Those are not my definitions.
> It's a straightforward logical inference. Your definition of capitalism excludes every capitalist economy that has ever existed
No. A social market economy is capitalism with rules and safety nets, like strong labor protections, healthcare, and pensions, to make sure people are protected from big hardships. The U.S. mostly has free-market capitalism, with fewer regulations and weaker social support. So the main difference is that a social market economy tries to control capitalism to protect people, while the U.S. mostly lets the market run on its own.