> Capitalism is not "the economic system in which things are bought and sold with money"
Well, at least according to Marx (c.f. Capital) capitalism is the system where things are bought and sold with money. If you read first few chapters of Capital you'll see that Marx explains this in various ways such as characterizing capitalism with division of labour where instead of producing bunch of commodities, workers produce one commodity and sell it for money with which they can buy other commodities. And according to, again, his definition communism is the society after this type of commodity production, i.e. the mechanism that produces value (money) is stopped in the sense that people stopped exchanging things for money.
You may not care of Marx's definition, but I just wanted to note for completeness.
Indeed, I don't defer to Marx. But that said, it's been a while since I read him much. I suspect you're conflating Marx describing Capitalism with defining it.
We can describe the idea of buying and selling with money as certainly being a characteristic of Capitalism without asserting that it's a defining characteristic that is absent in other systems.
To be blunt, buying and selling with money is FAR older than Capitalism.
I'm really sorry that I will not be able to provide any source to you at the moment because I'm very busy, but for what it's worth I'll write you what I remember from my readings (I studied Marxism extensively for a time out of interest but I never had a formal education in sociology, so I'm not an expert, I'm a regular software engineer). Also disclaimer, I tend to agree with Marx on a lot of issues so my ideas might be biased. My terminology is also a bit rusty.
Capital starts by explaining commodities. This is because: (1) Marx tries to explain some bit of the terminology of his period's economic terminology so he needs to do some ground work; (2) commodity production is an important aspect of capitalism that he refers all throughout his works. My main point is that the force that made capitalism possible and the force that sustains capitalism is one, which is the accumulation of value. As Marx explains in later chapters, a things will have different types of values. For Marx, nothing has any intrinsic value and its money-value is determined at the moment of trade. That is the force that generates value inside economy is the act of selling commodities. The same force causes the distinction between bourgeousie and prolateriat (c.f. Marx's definitions of social classes) and the same force caused the transformation from earlier economic system to capitalism (which answers your complaint). Now this brings us to the end of capitalism, which Marx very insistantly argues that end of capitalism is the seizure of value generation which is equivalent to saying society being moneyless. E.g. one misconception people have is that Marx was also against labor-vouchers, but this is not true, as explained in Critique of Gotha's Programme, since labor-vouchers do not generate/accumulate value, their value is not determined at the moment of trade. Anyway, this also relates to Marxist criticism of anarchism. For anarchism capitalism --> communism is the seizure of capitalist state. But Marxism thinks this is fundamentally wrong because capitalist state is generated by capitalist mode of production. So, you will want to eliminate the capitalist mode of production instead of the state itself, because as long as c.m.p exists there is no way to kill capitalism, so state will revive. For Marxism you first need to eliminate the economic system that makes capitalism possible, i.e. accumulation of value, and then ultimately kill the State and class society as they're caused by capitalism.
Well, at least according to Marx (c.f. Capital) capitalism is the system where things are bought and sold with money. If you read first few chapters of Capital you'll see that Marx explains this in various ways such as characterizing capitalism with division of labour where instead of producing bunch of commodities, workers produce one commodity and sell it for money with which they can buy other commodities. And according to, again, his definition communism is the society after this type of commodity production, i.e. the mechanism that produces value (money) is stopped in the sense that people stopped exchanging things for money.
You may not care of Marx's definition, but I just wanted to note for completeness.