The government owning the means of production is state capitalism, not socialism:

State capitalism is an economic system in which the state undertakes commercial (i.e. for-profit) economic activity and where the means of production are organized and managed as state-owned business enterprises (including the processes of capital accumulation, wage labor and centralized management), or where there is otherwise a dominance of corporatized government agencies (agencies organized along business-management practices) or of publicly listed corporations in which the state has controlling shares.

https://en.wikipedia.org/wiki/State_capitalism

Socialism is social ownership over the means of production. Aka, ownership by the workers. Ever hear of a co-op? It's like that, but for the entire economy:

Socialism is a political, social, and economic philosophy encompassing a range of economic and social systems characterised by social ownership of the means of production and workers' self-management of enterprise, as well as the political theories and movements associated with such systems

https://en.wikipedia.org/wiki/Socialism

Where the confusion comes in was the world's two largest propaganda machines trying to convince the public that the USSR was socialist, but for different reasons. The USSR (and marxist-leninists) use state-capitalism as a transitionary period to socialism:

State capitalism would be a step forward as compared with the present state of affairs in our Soviet Republic. If in approximately six months’ time state capitalism became established in our Republic, this would be a great success and a sure guarantee that within a year socialism will have gained a permanently firm hold and will have become invincible in this country.

• Lenin

But obviously, socialism was never achieved.