They were Communist, in the sense that it is commonly used today. But that isn't how Marx intended it - today, it is used for any country led by a Communist party. To Marx, it meant a society where everyone was equal, where governments had withered away and capital was owned equitably by all, working by the rule of "from each according to their ability, to each according to their need". Communist parties are so named because they seek to work towards this end.

Describing them as socialist is, however, fair. Socialist societies are defined by the fact that industry, and capital, are owned by labour, or representatives thereof. In the case of the Soviet Union, the government claimed to be representing labour. The amount to which they actually did can be debated, but I personally would describe the Soviet Union as socialist.

The USSR was officially Marxist since its creation. The early political development of the USSR and Lenin's policies shaped a ideology called Marxist-Leninism which was the official ideology of the Communist Party of the Soviet Union. The ideology builds on the transition from capitalism to socialism and finally to communism by refining the practices of the socialist transition state and how it would be guided. The development of a vanguard to lead the revolution and state was taken on by the Communist Party. The Soviets were not immediately trying to transition to communism, but build support for the global revolution which was believed to be necessary for communism to be achieved.

The failure of left revolutions after WWI left the USSR politically isolated and lead Stalin to declare the goal of building socialism in one state as sort of an example of how a possible revolutionary state might succeed and possible inspire other movements.

After WWII the Soviets and other communist movements began to gain traction and declare communist or socialist states which usually based their political policies on Marxist-Leninism and either developed their own policies or attempted to follow it. The Soviets then attempted to promoted communist movements in the new independent former colonial nations and developed countries in order to spread the revolution.

The end of the USSR meant that they never actually succeeded in spreading or creating a global revolution and never truly achieved global communism.