What is the difference between communism capitalism and socialism?

There is no ism called "capitalism". The word was adopted by Karl Marx to provide a contrast to his theory of socialism and be easily knocked down. That is called a strawman argument.

Many people assume that capitalism means free market, but it certainly does not mean that. The best definition of capitalism is "the way we do things in the west." Economics theory requires three things: land, labor, and capital. Capital is defined as tools of production. In the west, businesses are run on borrowed money, so the loan to buy tools is called a capital loan, and the word is then applied to any available funds. Throughout this process, the word has no well defined meaning.

Socialism is when the society owns the factories and runs them for their general benefit. Communism is when the factories are owned by a centralized government and they are run for political reasons. The only successful commune is Oneida and that is because of their silverware business. Amana held on for a while, selling refrigerators, but they sold the brand to Whirlpool.