First of all, neither the Soviet Union nor China were/are a classless society, since there was a ruling class (dictatorship) that oppressed the working class.
A common mistake is confusing dictatorship and totalitarianism. Dictatorship is a rule by one or few people, who control the mechanisms of power (e.g., via army, police, repression of anyone who could challenge their rule.) These do not constitute in class in Marxist sense. More importantly, dictatorships are usually unconcerned with how their subject live their private lives, what they say or which freedoms they exercise - as long as these activities do not threaten the power of the governing clique. One
Totalitarian society aims at remodeling everyday life according to certain model, aiming at all its aspects - what people eat, how they dress, what they discuss and think, how they celebrate important occasions, how they organize their economic relations, how/whom they pray. The well-known examples of totalitarian societies are the Communist, National-Socialist/Fascist, and Islamist regimes (as practiced, e.g., in Iran or Saudi Arabia). The nature of the totalitarian society was aptly captured by Orwell in 1984 and the Animal farm (both echoing the early years of the USSR) and more recently in The Handmaid's Tale.
The difference between Communists, National-Socialists/Fascists, and Islamists is the justification used for abolishing the individual freedoms - in the name of Class, in the name of Nation, or in the name of Religion. Abolition of individual freedoms in the name of class is the cornerstone of the ideology developed by Marx and collaborators, and various Communist and Marxist regimes were faithful to it. Marx also didn't hide that these goals were to be achieved via violence and suppression, as captured by the term dictatorship of the proletariat^1 - dictatorship by a class, rather than a group.
One could point at various points of divergence in details between Marxism as envisaged by Marx and its practical realizations. Unlike Hitler, Marx was not a practical man and never intended to implement his policies himself, so he didn't bother himself with the the logical consequences of his philosophy. In addition, most Communists regimes emerged well after the Marx' death, and had to deal with the realities that he couldn't even imagine. One could equally point out the differences in implementation of Marxist prescriptions in different countries, as exemplified by outright hostility and wars, like Sino-Soviet split. Yet, the essence remains the same - like Christianity does not become Islam just because there are divergences between Catholics, Protestants and Orthodox, and all three are different from how it was preached some 2000 years ago.
E.g., Marx didn't foresee emergence of a class of party functionaries, who would abuse their power rather than use it for the good of the population. Emergence of such a class is however an inevitable consequence of trying to implement his prescriptions on a scale of a country: The need for managing and distributing resources for millions of people, as well as managing their everyday lives, requires a bureaucracy of millions of functionaries - the notorious big government (as much as the term might be abused by the western right-wing, it was a reality in the communist and fascist states.)
Calling these countries socialist also doesn't work, since in a socialist society the means of production are shared collectively (at least to my knowledge), and in most countries that are called socialist
In the USSR the means of production were owned collectively - which in practice meant the ownership by the government, and supervised by the party functionaries, who consequently could use it for their benefit or for how they imagined the benefit of the population.
The confusion here is between the use of term socialism in colloquial discourse (in the meaning of social) and its formal meaning in political economy, notably as defined by Marx (a transition state between Capitalism and Communism.) Importantly, all the Soviet-aligned states formally declared themselves Socialist, whereas none of the modern western socialist states is formally defines itself as such.
For example, the Soviet constitution declared:
Article 1. The Union of Soviet Socialist Republics
is a socialist state of the whole people, expressing the
will and interests of the workers, peasants, and intelligentsia, the working people of all the nations and
nationalities of the country.
Article 2. All power in the USSR belongs to the
Article 3. The Soviet state is organised and functions on the principle of democratic centralism [...]
On the other hand, here is as the V-th French Repiblic is defined by its constitution
La France est une République indivisible, laïque, démocratique et sociale. Elle assure l'égalité devant la loi de tous les citoyens sans distinction d'origine, de race ou de religion. Elle respecte toutes les croyances. Son organisation est décentralisée.
(France is a indivisible, secular, democratic and social republic. It assures the equality before the law of all the citizens without distinction of origin, race, or religion. It respects all beliefs. Its organization is decentralized.)
I recommend reading the Soviet Constitution and some Marx for more enlightened view (at least the Communist Manifesto, which can be found in many languages and is relatively short.) While the modern Western economic and political systems can be criticized on many counts, there are more intelligent and less extreme solutions than Communism. The use of this term is usually a matter of an outright provocation or deep ignorance, comparable to flat-earthing, global warming denial, anti-vaccine movements, creationism, etc.
^1 Dictatorship of the proletariat is a Marxist term, despite some claims of its latter origin:
The socialist revolutionary Joseph Weydemeyer coined the term dictatorship of the proletariat, which Karl Marx and Friedrich Engels adopted to their philosophy and economics.
In Marxist philosophy, the dictatorship of the proletariat is a condition in which the proletariat holds state power. [...] During this phase, the administrative organizational structure of the party is to be largely determined by the need for it to govern firmly and wield state power to prevent counterrevolution and to facilitate the transition to a lasting communist society.
That is already the recipe for political repression, implemented by so many Marxist followers.
It is also interesting to see the list of euphemisms used to describe the dictatorship of the proletariat:
Other terms commonly used to describe the dictatorship of the proletariat include socialist state, proletarian state, democratic proletarian state, revolutionary dictatorship of the proletariat and democratic dictatorship of the proletariat.
Terms socialist state and democratic dictatorship are particularly echoed in the modern political discourse.
The Ten Points Of Marxism
Below is the 10 point program outlines by Marx and Engles in The Communist Manifesto:
Abolition of property in land and application of all rents of land to public purposes.
A heavy progressive or graduated income tax.
Abolition of all right of inheritance.
Confiscation of the property of all emigrants and rebels.
Centralisation of credit in the hands of the State, by means of a national bank with State capital and an exclusive monopoly.
Centralisation of the means of communication and transport in the hands of the State.
Extension of factories and instruments of production owned by the State; the bringing into cultivation of waste-lands, and the improvement of the soil generally in accordance with a common plan.
Equal liability of all to labour. Establishment of industrial armies, especially for agriculture.
Combination of agriculture with manufacturing industries; gradual abolition of the distinction between town and country, by a more equable distribution of the population over the country.
Free education for all children in public schools. Abolition of c hildren’s factory labour in its present form. Combination of education with industrial production, &c., &c.
All points of these program were diligently implemented by major communist states, notably the USSR. The only caveat is that some of these points, like
2. A heavy progressive or graduated income tax. and
3. Abolition of all right of inheritance., were made obsolete in the conditions of the complete nationalization of means of production, housing and nearly everything going beyond personal items - there was simply nothing to tax and nothing to inherit.
A relevant quote from the Historical dictionary of Marxism:
While the practice of these and other countries claiming to be Marxist would seem to be at odds with much of what Marx wrote, for example about freedom and the future stateless, classless communist society,it would be facile to dismiss any link between Marxism in theory and communist practice. For example, there is a case to be made for suggesting that Marx and subsequent Marxists neglected the individual, individual rights, constitutional checks and balances to power, and democratic institutions and procedures. This stemmed, perhaps, partly through too optimistic a view of human nature and a failure to observe Lord Acton’s dictum that “Power corrupts; absolute power corrupts absolutely.” The omission in the theory suggests a reason for the totalitarian tendencies displayed in communist practice.
Another quote, this time from Isaiah Berlin's biography of Karl Marx:
This doctrine (the clearest formulation of which is to be found in the
Address of the Central Authority to the League, written by Marx
and Engels in 1850) is familiar to the world because (revived by
the Russian agitator Parvus) it was urged by Trotsky in 1905,
adopted by Lenin, and put into practice by them with the most
literal fidelity in Russia in 1917.
The quote refers to the concept of permanent revolution and dictatorship of the proletariat, which Marx himself tried unsuccessfully implement during the Revolutions of 1848 (mainly through advocating such action via newspaper Neue Rheinische Zeitung, of which he was the editor.
Was there communism without the USSR?
Another way to look at the question is by examining of what the "real Communism" without the USSR looked like... more precisely - was there ever a Communist/Marxist movement without the USSR?
Communism before the Socialist Revolution in Russia
Surely, Marx and Engels wrote there foundation texts before the USSR came into being, and they have made two abortive attempts to establish it as a real political movement - via the International Workingmen's Association (First International) and the Second International. There had also been the German Socialist Party (SPD) which professed Marxist values, but which was plugged from the very beginning by fighting between the "revisionists", i.e., the adherents of the Parliamentary political engagement, and the Spartakists - the proponents of violent Marxist revolution, who would later split off to form the Communist Party of Germany.
Communism after the Socialist Revolution of 1917
After the Revolution the Communist parties suddenly emerged in great numbers in many countries, as can be seen from https://en.wikipedia.org/wiki/List_of_communist_parties. The rare cases where the party foundation date predates the revolution, like the Chilean Communist Party, turn out to be the cases of the existing parties suddenly changing their name and aligning to the Moscow orthodoxy. The above mentioned Communist Party of Germany also emerged after 1917, as a movement opposing "bourgeois" Weimar Republic.
A characteristic example is the French Communist Party - indeed, by then France had then a more than a century old socialist tradition, represented by such names as Saint-Simon, Joseph Fourier, Proudhon, Louis-Blanc and Blanqui - all of which influenced Marx. French Revolution, French class struggles, and ultimately French Commune were par excellence the standard cases in Marxist theory, as exemplified by Marx' classical works like Misère de la philosophie, The Eighteenth Brumaire of Louis Bonaparte, and The Class Struggles in France, 1848–1850. Yet, France didn't have its own Communist Party until this would be parachuted by Comintern.
Of course, some later communist movements would adopt clearly anti-Soviet Positions, notably China during the Sino-Soviet split. But logically, it is the rejection of the Soviet line which should be considered as not real communism, and not the other way around.