Merriam-Webster 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

2a a system of society or group living in which there is no private property
2b 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

In summary: totalitarian state without a private sector.