I know that they claim to be "communist", but how to these systems differ from one another?
The WGBH TV documentary presented in a totally false light the conflicts between the Chinese communist leadership and the Comintern. In the mid-twenties, the CI imposed a Menshevik conception of revolution on the young and pliable Chinese party. It ordered the CCP to liquidate itself into the Kuomintang, abandon social slogans, which alone were able to rouse the masses, and disarm itself, the trade unions in the cities and the peasant unions in the countryside. This policy was based on a petty-bourgeois interpretation of the old 1905 Bolshevik slogan "revolutionary dictatorship of the proletariat and the peasantry". Lenin discarded this slogan in April 1917, as he reoriented the Bolshevik party towards converting the democratic revolution into socialist. Lenin, in fact, adopted Trotsky’s conception of the permanent revolution.
But the show kept quiet about the strategic difference between the Marxist conception of permanent revolution based on a revolutionary government of workers and poor peasants led by the proletariat, and the Stalinist conception of revolution by stages, that is a democratic bourgeois revolution first, and a socialist revolution in the future. Instead, the show presented us with a detailed expose of a purely tactical disagreement between Stalin’s emissary to China, Otto Braun, and the Mao leadership. Braun was for regular war tactics, building orderly Red Army formations, defending fixed objects, cities, regions, etc. Mao was for guerrilla tactics, maneuvers, and so on.
This was the so called "Third Period" in the history of the Comintern. Having been forced to abandon the collaboration and "step at a time" line of 1924–28, Stalin embarked on forced collectivization in Russia and on ultimatist and sectarian "class war" policy elsewhere. In Germany, this policy called for attacks on the Social-Democrats, even when this split the workers’ movement and helped the Fascists. In China this line called for abandoning democratic slogans, instead calling for the building of Soviets, Red Armies, Soviet zones, etc. This worsened the sectarian isolation of the Chinese Communist Party and hastened its virtual decimation in the cities. The Third Period policies of guerrilla warfare had a further lasting effect: the Chinese Communist Party ceased to be a workers’ party and became a party based on the peasantry.
The Third Period lasted until 1934 in Europe, a bit longer in China. It led to the victory of Hitler in Germany and was quietly abandoned. The 7th Congress of the Comintern in 1935 proclaimed a totally different line, a policy of the Popular Front. The Communist parties were urged to form alliances with Social-Democrats, Radicals, democratic capitalists, trade union reformists, etc. The goal now was peace in Europe, opposition to Fascism, preservation of the status quo. The colonial question became subordinated to the diplomatic power politics of the Kremlin bureaucracy. Indian, Vietnamese or Indonesian Communists were ordered to develop their strategy according to how friendly their colonial masters (Britain, France and Holland) were to the USSR.
In China this policy required Mao to form an alliance with Chiang and the Kuomintang against the Japanese invaders. Although Chiang was extremely weak and isolated even within the Chinese bourgeoisie (in December 1936, in the famous Sian coup, he was kidnapped by military Nationalist leaders, who wanted to fight against the Japanese). Mao pulled Chiang’s fat out of the fire in this incident and delayed the victory of the Chinese Revolution by another 13 years.
http://web.mit.edu/people/fjk/essays/maoism.html
http://www.slate.com/id/2095043/
