The two have nothing in common. Communism is a political and economic theory that proposes that all means of production should be communally owned and avoid the presence of a class structure by creating a level of equality for all citizens. Buddhism is a religion based on achieving enlightenment by renouncing the unsatisfactoriness of the world and ascending to the temple of the mind.
One is a religion and the other is a political ideology.
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religion
There is no similarity between Buddhism and Hinduism though both of them are originated from India. Main difference is Hinduism believes in existence of God while Buddhism dont.
leaders of Hinduism worship God. While leaders of Buddhism do not worship God.
Buddha is not even born in India or china its born at Nepal only.
communism was focus on achieving practical political change
See: Communism.
Communism is a form of authoritarian government which was used in the 20th century to implement communism, a system of economic relations where the means of production are given to the proletariat and class distinctions are broken-down.
communist ruled by military democracy "governed" by the people
There are few elements about Zen Buddhism that are truly unique. Mostly the difference between Zen Buddhism and other forms of Buddhism is just a matter of emphasis. In Rinzai Buddhism, there are unsolvable questions called koans. These are unique, not found in any other denomination.
Buddhism does not believe in any difference between race, gender, age or caste. Therefore it did not and does not, support the caste system at all.