Assuming that the primary philosophical and economic model of use was that outlined in Marx's Communist Manifesto
They did not use the phrase "communist" because in classical Marxist political philosophy, a communist society would be the utopian end result of socialism. Marx outlined a general trajectory for society after the proletariat seized the means of production, but he was often hazy as to how and when a socialist state would achieve communism. Nor did post-Marxian socialist and communist parties have much of an idea either. The Bolshevik wing of the Russian Social Democratic Labor Party (RSDLP) soon renamed itself the Communist Party of the Soviet Union (CPSU- although there were some variations between the final naming) after the 1917 Revolutions to both differentiate itself from other socialist parties, but also to signify that the Revolution had achieved something new and was working towards this goal. But the even in its most hectic and ideological years, the CPSU never asserted the USSR had communism. Most of the CPSU and other Communist Parties asserted that their various campaigns were building socialism, not communism. Communism was the end goal of these various projects. The predicted advent of communism became one of the black jokes of the USSR as some Soviet leaders, most famously Khrushchev, predicted a specific date for the USSR to arrive at communism and these predictions never came true. Like many politicians, vagueness is the best option for grand promises they cannot deliver and many Soviet leaders did not appreciate this lesson.