That's the
definition of socialism: the government owns the means of production.
Definition of socialism
1 : any of various economic and political theories advocating collective or governmental ownership and administration of the means of production and distribution of goods
2 a : a system of society or group living in which there is no private property
b : a system or condition of society in which the means of production are owned and controlled by the state
3 : a stage of society in Marxist theory transitional between capitalism and communism and distinguished by unequal distribution of goods and pay according to work done
https://www.merriam-webster.com/dictionary/socialism
I guess you missed this part on your Webster link?
socialism vs. social democracy
In the many years since socialism entered English around 1830, it has acquired several different meanings. It refers to a system of social organization in which private property and the distribution of income are subject to social control, but the conception of that control has varied, and the term has been interpreted in widely diverging ways, ranging from statist to libertarian, from Marxist to liberal. In the modern era, "pure" socialism has been seen only rarely and usually briefly in a few Communist regimes. Far more common are systems of social democracy, now often referred to as democratic socialism, in which extensive state regulation, with limited state ownership, has been employed by democratically elected governments (as in Sweden and Denmark) in the belief that it produces a fair distribution of income without impairing economic growth.