You need a better dictionary. Webster’s is close but not complete. Where they define Socialism as “any of various economic and political theories advocating collective or governmental ownership and administration of the means of production and distribution of goods” the true definition would read “any of various economic and political theories advocating collective or governmental ownership or control of the means of production and distribution of goods.”
Some forms of socialism adopt a more pragmatic approach. Many industries are left in private hands — a recognition free-markets are more efficient in producing goods. However, the socialist society attempts to use progressive taxation and social spending to provide a minimum safety net. Important public services are run directly by the government.
This is obvious in Democratic Socialist parties where they have to win the next election to stay in power so cannot Nationalise Private property. Without absolute power they do what the electorate lets them do, regulate the economy, distort it by taxation and red tape, then tax the rich and redistribute the funds to the poor. These are all Socialist policies, but stop short of Government ownership of the means of production and distribution.
Or try an economics site such as https://www.economicshelp.org/blog/glossary/capitalism-v-socialism/
This site has definitions of Capitalism and Socialism:
“The main difference between capitalism and socialism is the extent of government intervention in the economy.” Hitler intervened in the economy, and tried to run it by committee: that didn’t work. so he allowed Speer to reintroduce Capitalism in the Arms industries, which increased the output by 500%.
“A capitalist economic system is characterised by private ownership of assets and business. A capitalist economy relies on free-markets to determine, price, incomes, wealth and distribution of goods.” This works, but is unpopular with leftists because the Rich get richer, and the poor get richer too, but not as fast.
“A socialist economic system is characterised by greater government intervention to re-allocate resources in a more egalitarian way.” That’s a generous definition of Socialism: when they say intervention, they really mean interference in the Free Market economy which generates the wealth, and by redistribution of that wealth, ensure there is less of it to go around. Once all incentive to create wealth is gone, it is not long before there is perfect equality — all are poor. This is the key feature of Socialism: Government contol of the economy, even without Government ownership, cannot work because central planning does not work: it always results in queues caused by shortages while shelves are full of things people do not want. Shortages and gluts can only be solved by the price signals of a free market economy working to balance supply and demand.
Socialist Governments whether run by Hitler, Mao, Pol Pot or Stalin never work. What about the People’s Republic of China? That is now a Capitalist country wearing Socialist Rhetoric: they have got rich since reintroducing the free market at the microeconomic level while retain Mafia style rigid control at the political level.