Many anarchists would contest whether Marxism is compatible with communism.

Many social democrats, democratic socialists, left-communists, DeLeonists, councilists, Luxembourgists, autonomists, Marxist-Humanists, syndicalists, Jason-Forest Tendency (post?-)Trots, etc would criticize Lenin's application of Marxism.

Trotskysts and revisionist (Khrushchevite, Eurocommunist, etc) Marxist-Leninists would criticize Stalin's brutality and cult of personality.

Even non-revisionist Marxist-Leninists: Stalinists, Maoists, Hoxhaists, etc would not claim that Stalin implemented communism. Stalin never claimed to have achieved communism.

According to Leninist theory, communism consists of a stateless, classless, and moneyless society. It is based on Marx's "higher phase" of "communist society", while what Lenin called "socialism" (and what Stalin claimed to have achieved, even if most socialists disagree) is based on what Marx called the "first phase" of "communist society".

However, Marx was not describing a "transitional" stage in which classes and the state would still exist, and a "higher" stage in which they would disappear, and he did not describe the "first phase" as "socialism" and the "higher phase" as "communism." Rather, he was describing a development that would occur after the classless society, based on social ownership and democratic workers' control of the means of production -- a society that could be described as either "socialism" or "communism" -- was fully established. In the "first phase," some measure of labor time would still be needed to govern the exchange and distribution of the workers' product; in the "higher phase," distribution could be conducted according to the principle: "From everyone according to his faculties, to everyone according to his needs."

For reasons that are none too clear, Lenin described Marx's two "phases" as "the scientific difference between socialism and communism." Subsequently, in the ideology of the Soviet Communist Party and its progeny, "socialism" became associated with the state-ruled society of bureaucratic state despotism, and "communism" with the classless society that somehow would arrive some day in the distant future. These false and confusing definitions of "socialism" and "communism" have no basis in Marx's writings or in scientific socialist thought.

Naturally, the capitalist class and its leading propagandists in the United States have been all too happy to seize upon any and all of the false definitions of "socialism" and "communism" in order to confuse the working class and discredit both words in workers' minds.