I'm glad you asked, because so rarely do we bother to define these terms. I'll give you an extra:

Capitalism: An economic system in which the the means of production and services are primarily controlled by private individuals.

Socialism: An economic system in which the the means of production and services are primarily controlled by the workers themselves.

Communism: An economic system in which the the means of production and services are primarily controlled by the government (AKA the organization with a monopoly on violence).

Are these the textbook definitions? Nope. But these are probably definitions most people would think of in a casual sense. If we were in an academic setting I might try to stick to academic language, but we're on the general internet, so....

Anyway, so it should be clear to you that there aren't any pure systems using these definitions. The US, a primarily capitalist system, does have government-run businesses and services, even ones that compete directly with privately owned organizations. (E.G. Amtrak, the postal service, libraries, schools, a few grocery stores and ISPs...) China, which I would argue is primarily capitalist at this point, does have government ownership or involvement in major businesses that goes beyond the broadly applicable regulations we see in most countries. But at this point most of their involvement is so light, I think the economy is functionally capitalist. A classic example is the real estate market. Everyone in China treats real estate investment as if it were actually privately held land, and not technically land that's on lease from the government for a long-ass time. It's so de-facto private that no one disgusting believes the government is going to make good on their leases when the terms are up. To do so would be economic suicide.