It seems that to you, capitalist simply means free market, and you call any kind of state intervention socialist. If those are the definitions, we probably agree.
However, that is not how those terms are normally defined or used. Capitalism means "an economic system where most enterprises are wholy owned by those who invest the initial capital". This differs from earlier economic models like feudalism, where enterprises were typically wholy owned by a lord through hereditary rule.
Socialism is normally defined as "an economic system where most enterprises are wholy owned by the workers who work in them".
Socialism can very well be a free market system, just like workers co-ops compete today with other worker's co-ops and more traditional capitalist corporations. Conversely, an economic system doesn't stop being capitalist just because there are tariffs or subsidies or other interventions by the state.
In particular, you can have a purely capitalist system with slave labor, since workers' rights are entirely irrelevant to whether a system is capitalist or not. In fact, freeing slaves has usually posed a problem to those with capital, and so the states that forced them to free their slave typically had to reimburse the owners for their loss of property as if they had nationalized a piece of land.
Later edit:
> Thank you, thats my point. They can't survive long unless they are supported by an authoritarian govt or by a weak govt.
My point about the weak government was that a powerful corporation faced with a weak government will just hire its own mercenaries and do what it wants, ignoring any law (usually forcing people to work) - like Chiquita and other banana companies did in South America.