This is actually an incorrect definition. Communism is the final state of socialism.

The problem with capitalism is that it inherently disenfranchises most people. It pits capitalists against workers in a tense arrangement where both sides are trying to gain the upper hand in negotiations over salaries/benefits. There are obviously more workers than capitalists. Capitalists own stuff that can be used to make more stuff. Workers own their own labor. Workers are the ones whose labor leads to the production of stuff.

Governments develop as a result of the tension between the two classes. They exist to mediate conflicts between the capitalists and the workers. However, politicians/rulers are traditionally drawn from the capitalist classes and capitalists are able to lobby governments for rules that are favorable to them. This is easier for capitalists because capitalists individually have more stuff to bribe the government with. Also the politicians and the capitalists tend to be from the same group.

This is obviously a problem because for the workers to get anything done favorable to them, they need to all agree on what needs to be done. Since there's more people in the working class, this is harder to do. There's fewer capitalists, so it's easier to get them all on the same page.

Marx predicted that this unfair relationship between the capitalists and the workers would lead to constant conflict between the two classes. Eventually the workers would win (just by numbers) and assume control of the government. Since the government is designed to support the capitalist class, that means that this would produce a lot of tension as trying to shift a government to favor the workers is difficult. A lot of the rules that the workers would try to implement won't really make sense in the context of a capitalist structure. This period immediately after the revolution is called "socialism". It's marked by governments trying to strike a balance between supporting capitalist structures but also enabling workers, which is very difficult to do.

Marx theorized that eventually society as a whole will realize that the two cannot truly coexist. We can't both support the masses and pursue profit at the same time. He theorized that eventually we will realize that the capitalist machinery(including the government, borders and nations) must be shuddered in order to truly free everyone. When that happens, that's when "communism" will begin.

All governments that call themselves "communist" are just "socialist" with the expressed goal of achieving communism.

The way you define it is part of the American red scare definitions which inherently tries to discredit communism and push workers to not rise up against their bosses.