China

in addition to the excellent China Has Billionaires which Yogthos already linked you, read this explanation as well

What makes a country "socialist"?

A society where public ownership of the means of production, a state controlled by a politically organized proletariat, and production for societal use rather than for profit is the principal aspect (main body) of the economy.

Key term here is principal aspect. There is a weird phenomenon from both anti-communists as well as a lot of ultraleft and leftcom communists themselves of applying a "one drop rule" to socialism, where socialism is only socialism if it's absolutely pure without a single internal contradiction. But no society in the history of humankind has been pure, they all contain internal contradictions and internal contradictions are necessary for one form of society to develop into the next.

If you applied that same logic to capitalism, then if there was any economic planning or public ownership, then capitalism would cease to be "true capitalism" and become "actually socialism", which is an argument a lot of right-wing libertarians unironically make. The whole "not true capitalism" and "not true socialism" arguments are two sides of the same coin, that is, people weirdly applying an absolute purity standard to a particular economic system which is fundamentally impossible to exist in reality, so they then can declare their preferred system "has never truly been tried". But it will never be tried ever because it's an idealized form which cannot exist in concrete reality, actually-existing capitalism and socialism will always have internal contradictions within itself.

If no idealized form exists and all things contain internal contradictions within themselves, then the only way to define them in a consistent way is not to define them in terms of perfectly and purely matching up to that idealized form, but that description merely becoming the principal aspect in a society filled with other forms and internal contradictions within itself.

A capitalist society introducing some economic planning and public ownership doesn't make it socialist because the principal aspect is still bourgeois rule and production for profit. This would mean the state and institutions carrying out the economic planning would be most influenced by the bourgeoisie and not by the working class, i.e. they would still behave somewhat privately, the "public ownership" would really be bourgeois ownership and the economic planning would be for the benefit of the bourgeoisie first and foremost.

A similar story in a socialist society with markets and private ownership. If you have a society dominated by public ownership and someone decides to open a shop, where do they get the land, the raw materials, permission for that shop, etc? If they get everything from the public sector, then they exist purely by the explicit approval by the public sector, they don't have real autonomy. The business may be internally run privately but would be forced to fit into the public plan due to everything around them demanding it for their survival.

Whatever is the dominant aspect of society will shape the subordinated forms. You have to understand societies as all containing internal contradictions and seeking for what is the dominant form in that society that shapes subordinated forms, rather than through an abstract and impossible to realize idealized version of "true socialism".

Countries like Norway may have things that seemingly contradict capitalism like large social safety nets for workers funded by large amounts of public ownership, but these came as concessions due to the proximity of Nordic countries to the USSR which pressured the bourgeoisie to make concessions with the working class. However, the working class and public ownership and economic planning never became the principal aspect of Norway. The bourgeoisie still remains in control, arguably with a weaker position, but they are still by principal aspect, and in many Nordic countries ever since the dissolution of the USSR, the bourgeoisie has been using that dominant position to roll back concessions.

The argument for China being socialist is not that China has fully achieved some pure, idealized form of socialism, but that China is a DOTP (dictatorship of the proletariat) where public ownership alongside the CPC's Five-Year plans remain the principal aspect of the economy and other economic organization is a subordinated form.

—zhenli真理

I actually like how I heard Hasan explain it once: billionaires’ wealth in China is similar to how farmers hold land there. All the land is owned by the government, but you can lease it and make money on it. Billionaires in China are merely holding onto some of the wealth of the nation. It ultimately belongs to the people and if the peoples’ representatives decide you should no longer hold it, you won’t have it anymore.

here's how https://redsails.org/china-has-billionaires/

"communist"

the way you are throwing this around makes me think you don't understand the distinction between achieving communism and a socialist state ruled by a communist party, so you should also read this:

Marxists argue that we should treat socioeconomic development as a field of scientific study, so we can develop objective theories to explain societal development since the dawn of human civilization to today, to understand how it developed, how it is currently developing, and to try and predict what it is developing into.

The purpose of any science is not to simply understand, but to control. We learn about electricity not to just understand the cause of lightning, but to control and harness the power of electricity to build new technologies and such to benefit human civilization.

Hence, the purpose of developing these theories is to form our politics around them so that we can facilitate socioeconomic development, to continually push humanity forwards into the future.

Most political parties with "Communist" in the name are Marxist-Leninist parties, and Marxist-Leninist distinguish between two ideas, "socialism" and "communism."

Communism is not a system anyone has ever implemented. The USSR was the Union of Soviet Socialist Republics. From Mao until today, the CPC has described China's system as a socialist state, not a "communist" one.

If Communist Parties in practice never establish communism, why do they call themselves "Communist"?

Because "communist" refers to extrapolating Marxian theories on human societal development as far as they can go, i.e. it is the theoretically most developed society possible. It is basically like a post-scarcity, Star Trek esque futuristic society that has such an abundance of wealth people don't have to work as a means of survival anymore but only work as a means to fulfill themselves as human beings.

It is best to think of "communism" thus as more akin to "futurism." A futurist is someone with an extremely positive, forwards-looking vision into the future, and wants to do things in the here-and-now to help push us in that direction. It offers an optimistic vision to encourage development in that direction.

Communist Parties are Communist because they are forwards-looking, they always have a more positive vision of the future they want to move towards, and never want things to "remain the same." It is part of China's constitution that the Party has to always develop the forces of production.

Meanwhile, "socialism" is what Marxist-Leninists actually advocate to implement in the here-and-now. You can't "try" communism, as if you just implement an arbitrary set of policies and you have "communism." It's something you build towards over the combined work of many many generations.

While Marxist-Leninists make the distinction between "socialism" and "communism," Chinese Marxists additionally add the distinction between the "primary stage of socialism" and "developed socialism," arguing that China has not even finished constructing socialism and is still in an underdeveloped, primary stage. They also tend to be critical of Soviet Marxists who had argued socialist construction was completed and they were on their way towards communism, viewing this as unrealistic and not a correct analysis of their current conditions, which led them to implementing bad policies.

Given that we will likely not see "communism" any time in the near future, probably not even in a hundred years, it is best to think of communism more as a futuristic philosophy, looking towards the future, than a specific system you implement. It's the reason why the USSR and China launched massive industrialization campaigns and became manufacturing superpowers. No, they didn't achieve "communism," but that's not the point, they point is they achieved something, they propelled their societies into the future.

China is only "Communist" in the sense that it has one of these future-oriented parties at the helm, constantly trying to drive China towards the future. But its actual economic system is not communism, but it is a rudimentary form of socialism, in the primary stage of socialism.

Marxist communists are future-oriented people who believe in using science and reason to steer the ship of human civilization towards a better tomorrow.

We must recognize that our labors today and the unceasing work of so many generations in the future are paired together, all moving towards the ultimate goal of achieving communism. If we throw away our Communist Party’s lofty ideals, we will lose our direction and become coldly utilitarian. At the same time, we must recognize that the realization of communism is a very long historical process. We must ground ourselves in the struggles of the present moment and keep our work down to earth.

—Xi Jinping, Speech at the Central Committee for the 18th National Congress of the Communist Party of China.

To care about the immediate interests only while forgetting the lofty ideal will result in the loss of direction of progress. But to talk big about the lofty ideal without doing any practical work will get one divorced from reality.

—Jiang Zemin, Speech at the meeting celebrating the 80th anniversary of the founding of the Communist Party of China

—zhenli真理