I accept your point on the American definition of socialism, which is a grotesque distortion of the truth, deeply ingrained in the US vernacular. This of definition eliminates capitalism entirely which is ridiculous. Why do you call China, Denmark, France or Germany communist or socialist when they operate McDonalds in all those countries? Obviously the US definition has no real world example that can be pointed to anywhere with the possible exception of Iran or North Korea and there only because US sanctions prevent trade. Its likely that other entrepreneurs operate there as well.
Do you now claim China, Canada, Germany and Russia are all now capitalist States? Because they all contain elements of Capitalism. Just as they all contain elements of socialism. And there's nothing wrong with that. The real problems always revolve around corruption, dictatorship, police States...
The US definitions are total BS, engineered by the 1% in their endless class war against workers. The purpose is to vilify the word, As they have accomplished with the word "liberal". The purpose is to take control of all property which has income earning potential, especially monopoly services and markets.
But Government ownership of natural resources, water projects and generating stations, schools, roads military bases are common in this and every other country, yet Americans continue to insist we are not socialist and never want to be socialist. The war against socialism is really a war over the meaning of the word, which has had little impact on how governments operate until extremists like Thatcher and many US Republicans sell off public assets to private interests. The result is always higher costs for consumers. If thee Capitalists did not see an opportunity to monopolize service or market they would have no incentive to buy the properties.
Socialism: a theory or system of social organization that advocates the vesting of the ownership and control of the means of production and distribution, of capital, land, etc., in the community as a whole.
Communism: a theory or system of social organization based on the holding of all property in common, actual ownership being ascribed to the community as a whole or to the state.
So the labeling of any country as just socialist or capitalist is all BS because every country is a blend of both.