Socialism in its original conception was a system of common (social) ownership (de facto possession - control, not just legal title), direct democratic control of production and free access to goods and services - the so-called socialism and communism systems of Asia and Eastern Europe had none of these attributes. Production was/is controlled by centralised state authority (as state-owned industries in mixed economies). The purpose of production in these countries was to create surplus (as in the west) for the bureaucratic elite who constituted the ruling class. In real socialism there is no state, no centralised bureaucracy, and no classes because there is common ownership and free access to all goods and services. The economic system of the USSR has much more in common with the mixed economies of USA and UK. The USA so hated the USSR and other state capitalisms (and fought militarily, ideologically and economically against them) not because of a clash of civilisations but because they were in competition. The USA does have state-owned industries and services and controls markets, therefore if Russia was socialist then so is the USA and UK by your definition.

Capitalism is the system of production for profit, minority (state, corporation or individual) ownership of the means of production and allocation of goods and services according to ability to pay. Capitalism is the main mode of production throughout the world.