Answer:
Anarchism and Communism are both subsets of radical Socialism.
Similarities
Both reject private property on the means of production and Capitalist state as the tool of oppression. Both embrace class struggle as the way to equality and more harmonious, just society.
Differences
However, Anarchists reject the State entirely. Once given a chance, they want to destroy it as an unredeemable evil, the eternal source of oppression. Everything the State does, must be devolved to self-governing collectives of workers and peasants. They then would arrange things on the national and global basis through horizontal networks of cooperation and arbitration.
The State
Communists, as true Marxists, view the State as an important tool in the transitional period between Capitalism and Communism. The State must take over the ownership over all or most of the means of production, introduce universal rights like the right to job, education, health care, maternity protection and suchlike. It must also create a powerful military-industrial complex to fight the Capitalist surroundings.
Evidence
History of the 20th century clearly proved superiority of the Marxist approach. Communists took power in several countries and managed to retain it in the face of much adversity. Anarchists are stuck in fumbling around purely economic experiments in countries like Spain, Mexico, Syria and Israel that are confined in tightly managed communities and do not really step outside the framework of Capitalist cooperation.
Explanation:
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