A classless stateless society is Socialism.
Communist
Nazism has of course no connection at all with Socialism, which means a classless stateless society based on production for use.
China is a republic, and is not Communist. Communism means a classless stateless society based on production for use, and would have to exist at a global level.
Such an economy is called a MIXED ECONOMY.
The former Soviet countries used to be examples of state capitalism, but are now mostly private capitalism.
Marx referred to the dictatorship of the proletariat as a temporary transitionary phase during which the working class seizes control of the state to dismantle capitalism and establish a socialist society. In this phase, the proletariat holds political power to reshape the economic system and ultimately achieve a classless society.
Marx envisioned a classless society as one where there is no social stratification based on ownership of the means of production. He believed that in this society, all individuals would have equal access to resources and share the benefits of their collective labor without exploitation. Marx saw the abolition of class distinctions as essential for achieving a more equitable and just society.
After World War I, The Russian Empire ceased to exist, giving rise basically to the Soviet Union (not mentioning the pro-Tsarist White governments during the Russian Civil War), which was officially the first Marxist government.
In February, 1917, riots broke out and a lot of workers went on strike. When the army joined the riots, Tsar Nocholas gave up his throne. A temporary government was set up. It wasn't able to solve the problems, and on 25 October, 1917 (According to our calendar it was on 7 November), the Bolsheviks led by Vladimir Ilyich Lenin, seized power and took control of the country. It was a socialist revoulution. (The new society was called socialism which was considered a transitory system of government before achieving Communism. Socialism was the dictatorship of the Proletariat.)
First of all, after the communism fell in the Soviet Union there was no more Soviet Union, it fell with communism, and secondly, it went way worse for most of the citizens, now there are many Romanians travelling to socialist countries close to them like Spain.
Karl Marx developed a system of equality called communism, which advocates for the abolition of private property and the establishment of a classless society where wealth and resources are shared equally among all members.
Many, but perhaps Karl Marx was most notable for that in his book, "The Communist Manifesto".
Anarchists were socialists and still consider themselves to be socialists. Anarchists opposed what is today called "state socialism", meaning any type of socialism that advocates for state ownership of the means of production as a form of social ownership. Liberals, conservatives, fascists and monarchists generally opposed socialism.