No, 'capitalism' and 'socialism' don't define economic systems
Lessons learned in youth persist throughout the years. The infant cannot define the words "mama" or "dada," but — in what may be the ultimate etiology of the practice of magic — he soon learns that uttering those sounds in a chortle produces tangible rewards, and thereafter learns to apply this lesson to other theatres of his relationship with parents.
Those of us who grew up in a Norman Rockwell painting were privileged to attend college during the American post-war golden age. One of our sacred institutions was the dormitory bull session.
Fifteen or twenty of us would gather in one of the dorm's lounges and engage in wholly unstructured debate on a variety of topics: politics, religion, philosophy — whatever struck our fancy. The proceedings were always entertaining and sometimes enlightening but inevitably collapsed into adjournment when someone committed the mortal gaffe of demanding that his antagonists define their terms. Thereafter, the correct definition of the terms "democracy," "communism," "capitalism," "socialism," "evolution," etc., became the focus of the debate. The inability to forge agreement terminated the bull session 'til next time.
The key idea is to understand that many words and phrases have both cognitive and emotive meanings and that many people use words solely for their emotive effect without regard to any cognitive component. They will eagerly enter into a discussion using the terms "communism," "capitalism," "socialism," "dictatorship," "authoritarian," "fascist," etc., with no clear cognitive meaning in mind. If you have any nonfiction books on your shelf with any of those words in the title, go to the index and see whether the author anywhere defines those words. If he does not, it signifies that his use of those words is intended to cause a buzz in your nervous system rather than to engage your intellect.
Against this background, I note that the phrases "law and order" and "rule of law" are commonly used as though they are synonyms, which they certainly are not. "Law and order" is what you get from Marshal Dillon; "rule of law" is what you get from the Constitution. The principal word in the phrase "law and order" is the word "order," meaning order under the police power of the state. The principal word in the phrase "rule of law" is "rule," meaning it is the law that rules, not men.
Image: Dictonary by fabrikasimf. Freepik license.
Similarly widely accepted is the idea that "capitalism" and "socialism" are two systems of economics. In reality, there is only one system of economics, and it doesn't have a name.
Economics is the art of creating wealth. The only way to create wealth is to start with some wealth — the startup wealth — which may be ships and factories or, maybe, only a man's strong right arm. Then, add to that a business plan, labor, management, and the realization of profit. There is no other way.
"Socialism" and "capitalism" are not systems of economics; they are systems of government. When people note that "socialism doesn't work," they mean "wealth creation doesn't happen under a socialist form of government."
After Mao's death, the Chinese realized that "socialism doesn't work" and that they could create wealth only by allowing a capitalist form of government to some degree. The problem was how to allow some degree of capitalism while maintaining dictatorial control.
The Chinese call their solution "capitalism with Chinese characteristics." The essence of this is to allow specified property ownership and free enterprise for wealth creation while maintaining total political power in the Chinese Communist Party and coming down hard on any signs of political independence. The deep states and elites around the globe (including the USA) have noticed that the Chinese have been remarkably successful and view the Chinese model as preferable to the American model.