China Communism

The Communist Party of China, or the CPC, is the the ruling political party of The Peoples Republic of China. Although it does work aside a coalition of governing bodies it is, in practice, the leading political party in the PRC. The party was originally founded in 1929 in Shanghai but it assumed control of mainland China in 1949. The other party retreated to Taiwan where it still stands today. The brand of communism the the PRC used was the Marxism-Lenninism brand (similar to Cuba's). China was connected with the Soviet Union until the 1960's when China and Soviet Union split up over ideological differences. The Communist Party's ideology was redefined under Deng Xiaoping to incorporate principles of market economics, and the corresponding reforms enabled rapid and sustained economic growth. 

Today the CPC is the largest political party in the world, claiming more than 80 million members (about 6%

of mainland Chinas population). Since 1978, the Communist Party has attempted to institutionalize transitions of power and consolidate its internal structure. The modern party stresses unity and avoids public conflict while practicing a pragmatic and open democratic centralism within the party structure.

Cuban Communism

Cuba has had a "communist" party in Cuba since the beginning of "Cuba" but the formal communist party was formed in 1925 by Moscow-trained members of the Third International.
For three years Cuba adhered to the Stalinist brand of Communism but between the the 1940's and 50's it collaborated with the government of Fulgencio Batista and no longer became communist. They renamed the party in 1944 to the Peoples Socialist Party. This was the  name of the party until 1961, when Castro overthrew Batista, when it was then named Organizaciones Revolucionarias Integradas. This was until, again. it was renamed (and recognized) as the United Party of the Cuban Socialist Revolution. This then dissolved and turned into the Communist Party of Cuba which was more along the lines of the Soviet Communism. In 1975 Cuba made it so that there was only one sole legal political entity. In a congress in 1991, in Cuba, they reaffirmed the sole legal political entity "rule". They did this because of the collapse of the Soviet Union and other Communist countries in eastern Europe.