After the October revolution, workers organized into free Soviets and established democratic worker’s self management. There were numerous parties including Bolsheviks, Mensheviks, Left-Socialist Revolutionaries and anarcho-syndicalists. The Bolsheviks cheated Soviet elections and became power hungry, forcefully crushing opposition such as left-communists and anarchists and establishing one-party rule under a vanguard state. Lenin and Trotsky believed the state should manage production rather than the unions, and they thought the rule of the Bolshevik Party would protect Russia from counter revolutionary or reactionary takeovers.
Before the revolution, Marxists and anarchists debated during the days of the First International about the role of the state. Marxists supported the idea of a transition state, which would take proletarian control of capitalism, produce socialism, and then the state would outlive its usefulness and be abolished to establish communism. Anarchists opposed the necessity of a transition state, and argued it could only be used as an institution for oppression and exploitation by privileged rulers. I tend to agree with the anarchists on this one, but the important thing is all communists agree communism will be stateless, they just disagree on how to get there.
So no, communism is not just one-party dictatorship of the proletariat, following Leninist democratic centralism alongside market socialism (or state capitalism depending on how you view it). There are also autonomous Marxist and libertarian communist movements, such as those in the Zapatistas and Rojava, and anarchist revolutions of the past in Ukraine and Spain.