Many people seem to have trouble with understanding what capitalism is exactly. Capitalism is based around the type of property named "capital". Capital is an asset owned for investing in laymans terms. For people more understanding of political theory it can be expanded on more deeply. Capital is control of the means of production by an outside force in which the controller extracts resources from the laborers. This can be done because there is typically no means of production in a capitalist society that are not called capital and controlled by this outside force. (States in their defense of capitalism will often violently attack any group that does not conform to this control, either by controlling their own property for their own use or trying to break the outside control of capital.) The resources taken from this labor, called profit, is then mostly used to expand the controlled capital, leading to an accumulation over time. The more capital controlled by an individual or group the more efficient it tends to become (at producing profit, not creating resources). This means that those with small amounts of capital not resorting to the worst tactics are often left in the dust and are essentially on the path to becoming another worker. (Fun fact fascism rises as a result of the middle class becoming poorer in this situation).
Capitalism is not just an economy where people interact, capitalism is not just an economy with a market, and capitalism is not just an economy where people produce things for profit. Capitalism is an economy based on the type of property capital.
People interact in every system. Market socialism, mutualism, and other economic systems have a market, and can produce things for profit.