This is a rather reductionist view of capitalism, socialism, and communism. To understand these systems, we need to take a look at the actual literature.
In 1776, Adam Smith published his work “An Inquiry into the Nature and Causes of the Wealth of Nations,” which defined the cornerstones of capital, money, and value theory in the context of the changing economies of the 18th century. Smith’s work is known for concepts such as “the invisible hand” and “competition prevents exploitation” through free market capitalism.
In 1867, Karl Marx published his work “Das Kapital,” which offered a critique on some of capitalism’s theories. This work provided the foundation for work on class theory, class struggle, and the notion of socialist/communist states. The key definitions being that capitalism separates the workers (who contribute labour) from the capitalist class (who contribute capital and thus machines and forces to improve productivity) and that socialist states place increasing control of these productive forces in the hands of the state (as opposed to the capitalist class). The other key work towards these notions is “The Communist Manifesto,” written with Friedrich Engels. The slogan “From each according to his ability, to each according to his needs” is perhaps the most representative.
Following Marx, Vladimir Lenin wrote critiques of capitalism and described how revolution could be used to achieve a socialist and (eventually) communist society. Mao Zedong’s writings discuss the ideas of revolution to achieve socialism and communism from a Chinese perspective, rather than the Russian one that Lenin had. Crucially, while Marx had written on the socialist transition as one for the advanced capitalist societies of Germany and England, Lenin and Mao approached it more from the perspective of how socialism could be realized from the predominantly agricultural economies of Russia and China.
In 1936, John Maynard Keynes published his work “The General Theory of Employment, Interest and Money,” which looked at savings and consumption in the context of the Great Depression. This work forms the foundation for much of modern fiscal and economic policy in the West. Keynes called for government intervention in support of the economy, deviating from Smith’s notions of a free market.
Perhaps the most relevant ideas on the topic today are from Deng Xiaoping Thought, which provided concrete ideas of developing Chinese socialism in the context of a capitalist global economy and in the context of China’s predominantly agricultural economy. This work was kick-started by “Putting into Effect the Socialist Principle of Distribution According to Work,” which described how China was unable to make progress from the primary stage of socialism due to the lack of productive forces which could be leveraged. Remember that Marx’ writings were written from observations of the great industrialized European powers, not the perceived agricultural backwaters of Russia and China.
The crucial concept of Deng Xiaoping Thought is the idea of a socialist market economy. Crucially, that socialism inherently involves the elimination of poverty (pulling people up) rather than the moderation of productivity (pulling people down). As per Keynes, a planned economy with government intervention does not preclude capitalism, and the lack of one does not preclude socialism. Indeed, per Keynes, public ownership of property did not preclude capitalism, and by extension Deng Xiaoping Thought argues that private ownership of property does not necessarily preclude socialism. Indeed, Engels work on the subject discusses that the abolishment of private property cannot happen immediately, and instead proposes alternatives (progressive taxation, inheritance taxes, development of state-owned enterprises) in the meantime for those countries struggling to get past the primary stage of socialism.
Just as a true Smithian free market capitalist economy does not exist, a true Marxist end-stage socialist economy does not exist. If you’ve any interest in this space, the works of Smith and Keynes on one side and Marx, Engels, and Deng on the other side provide pretty complementary coverage of things. In this framework, Smith, Marx, and Engels can be treated as one group (laying the foundations of the work) while Deng and Keynes can be treated as the ones building on top of those core ideas to adapt them to the realities of the situation (for Deng, China’s agriculturally-dependent economy, and for Keynes, the Great Depression).
In practice, we can see the obvious differences between the American and Chinese economies. Whereas the US economy is led by giant multinationals, China’s is led primarily by SOEs. Whereas US billionaires who hold productive forces are essentially invulnerable to government prosecution, Chinese billionaires are not. Whereas land in China is either owned by the state or by farmer collectives, land in the US is mostly privately held.