Marx and Engels shared essentially the same goal. In the stateless, classless, society of communism, the means of production would be held in common (by the community), work would be carried out due to social motives rather than for wages, and consumer goods would be available to all according to their needs.
Lenin divided communism, the period following the overthrow of capitalism, into two stages: first socialism, and then later, once the last vestiges of the old capitalist ways have withered away, stateless communism or pure communism. Lenin based his 1917 work, The State and Revolution, on a thorough study of the writings of Marx and Engels. Marx uses the terms the "first phase" of communism and the "higher phase" of communism, but Lenin points to later remarks of Engels which suggest that what people commonly think of as socialism equates to Marx's "first phase" of communism.
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