Under communism, all real and much personal property is owned by the state; everyone in the whole country must do what a central planning board directs them to do. That board cannot know local conditions nor how condidions differ from one locality to another, so its directions are often wrong. The workers and the manufacturers of the country in how they choose to allocate their time, labor, and other resources, are reacting to political incentives instead of market incentives. (Market incentives are given by customers; political incentives by laws and central planning boards.) Therefore they often do not produce what anybody needs or they produce poor goods that are of little value. For these and other reasons, a communist economic system cannot create wealth, at least not enough to sustain itself. It must constantly conquor new territories to exploit or suffer famines.
Capitalism leaves many of the characteristics of a free market in existence, and capitalism preserves many aspects of private property. Capital means money and property that is surplus to immediate needs for consumption, and, thus, available for investment in efforts to create more wealth. However, the term capitalism is not synonymous with private enterprise. Capitalism has never been content to live on only the wealth that it creates. Capitalism covets the wealth of others. Capitalism exists to harness the power of government for purpose of transferring wealth created by farmers and small business men, and others, into its own pocket. It uses tax structures, government regulations, government programs, imaginary wealth represented by paper documents, etc., for doing this. It is all therefore legal.
The two systems are pretty much opposites of each other -- that's how they relate.
If we are just talking about economic systems, the difference between the two is this: in capitalism, people own property and do what they want economically. In communism, the government controls pretty much the whole economic system.
In capitalism, for example, we have companies that decide what they will try to make and sell. If people want to buy the things they make, they will do well. If people don't like their stuff, they go broke.
In communism, the government owns the factories. Government officials decide what will be made. If people want the stuff, fine. If they don't it still gets made.
In theory, communism is supposed to make people equal. Everyone is supposed to get paid what they need so you don't have rich people and poor people like you do in capitalism. This has never really worked out in any communist country, though.
Communist countries have never been able to succeed economically. Most people say this is because the people of those societies have no incentive to work hard or invent new things. They can't get rich, so why try hard?
Capitalism is an economic ideology that promotes a profit oriented economy. You are able to sell a product based on the demand for it. If there is a high demand but a low amount of product, the price may be higher. If the product is plentiful, demand must be created to drive up the price. The business owners are private individuals or corporations. This model began to take precidence around the middle ages 1300s or so and really took off during the age of exploration 1600s through 1800s. The problem with capitalism is the ups and downs of the markets are not cushioned by the government. There is no concern for the "common welfare" or common good. It's just business. Lay-offs, bankruptcies, bank failures etc...are all just a part of the fluctuations of the market economy.
Communism was established as an ideology to help the working class gain wealth and power. It was developed during the Tsarist era in Russia to allow the workers to have a voice, ownership, and ability to live well on their wages. The totalitarian rule of the Tsars in Russia gave rise to the ideologies espoused by Karl Marx and Friedrich Engles.
In a purely communistic form of government, there would be no private ownership of land, production, or goods. Everyting would belong to the government (ie workers or laborers), and the government would then equitably distribute the rewards of the labor to the workers. Workers would be compensated according to their "value" to the overall benefit to society. There would be no health care shortages, no housing shortages, and everyone would have what they needed to live.
But no worker would be paid very much more than any other worker. There would not be any getting rich while making another poor. The ideal communist society would eliminate poverty by providing for the "common welfare".
The problems with communism in practice are that it does not encourage creativity or working to improve a system because the wages are not going to encourage more effort. Because the government runs everything, not all areas of an agricultural country will be able to have "planting day" on the same day. Finally, party members became the "privileged class" rather than the egalitarian society that they espoused. The party members were just as corrupt as the Tsarist regime that they overthrew to gain power.