I can understand the confusion over the term. Part of the problem is that socialists don’t always use the term consistently. Sometimes they use it to refer to states like the Soviet Union that own all the property, and sometimes they use it to refer to more of a social democratic “interventionist” state. Lenin himself even used the term to describe the Soviet Union. However, he meant something quite different than his socialist critics. He used it merely to indicate that the state was tolerating some private ownership at the time.
There is probably also a difference between how anarchists and libertarian Marxists define it. It would probably be easiest to understand the term from the Marxist side because their economic theory is more cohesive.
One of the problems is what is meant by “private” and “public” property. We often think of property with a legal title held by individuals or businesses as private and property with a legal title held by the state as public. It is often assumed then that a society where all of the property is public in this sense is socialist. In that case, libertarian socialists do not support public property. However, there is also a different way to divide property, by the way that it is open to use. We might use the terms “communal” property and "hierarchical " property to designate this difference (of course there would still be room for property which is neither communal or hierarchical but “individual”). The problem is that this second division often seems to coincide with the first division. For example, a city-owned park is communal because anyone is free to use it and is public because the government has legal title to it. But then there is also privately owned property that could be considered communal. Zucotti Park that housed the OWS protesters is a private park but is open to the public in the same way that a state owned one is. One might also consider a church library or a user operated site like Wikipedia to be communal despite being privately owned. On the other hand, battleships, public schools, and post offices are all public property but are hierarchical. It is therefore this communal property (in opposition to hierarchical property) that characterizes libertarian socialist society and not public property. (See Ivan Illich’s “Institutional Spectrum” for more on this distinction).
Let’s look at what some Marxists have said about “state capitalism.”
The best argument I’ve found so far that the USSR was capitalist is this article by Raya Dunayevskaya. She makes the point that private property is not what characterizes capitalism:
It is neither titles to property nor motives of individuals that distinguishes different exploitative economic orders, but their method of production, or manner of extracting surplus labor. If it was the legal title to property that were basic, the Stalinists would be right in assuming, “Since there is no private property in Russia, there is no exploitation of man by man.”
Behind the imposing façade of the “socialist economy”, however, stands the “classless intelligentsia”. The specific weight of the upper crust, as we saw in Part I, comprises a mere 2.05 per cent of the total population!
The individuals who act as agents of the state and its industry are, of course, theoretically free to refuse to participate in the process of accumulation, just as a capitalist in the United States is free to sign away to the workers in his factory his legal title to the means of production. In the United States he would retire to Catalina Island or, at worst, be sent to an insane asylum. In Russia he would be “liquidated”. But he does not refuse. He acts exactly as the agent of capital that he is, as agent of the dead labor alienated from the worker and oppressing him. The class difference between the two, which the Russians euphemistically call “functional”, is expressed outwardly, too, in no different manner than under traditional capitalism, where the one lives in luxury and the other in misery. It is true that in Russia the agent of capital does not “own” the factory. But personal property is recognized in the unlimited right to purchase interest-bearing bonds, sumptuous homes, datchas, and personal effects. State bonds, no matter how large the amount, are not subject to inheritance or gift tax. All forms of personal property can be left to direct descendants. Institutions of higher learning, the tuition fees of which make them inaccessible to the proletariat, welcome the children of these property-less factory directors, and this assures their offspring of good positions as befits the sons and daughters of the ruling class. This, however, is entirely incidental to the relationship in the factory.
It is not the caprice of the bureaucracy nor the “will” of the individual capitalist in competitive capitalism that sets the wages of the workers. It is the law of value which dominates both.
The law of value, i.e., the law of motion, of the Russian economy has led to the polarization of wealth, to the high organic composition of capital, to the accumulation of misery at one pole and the accumulation of capital at the other. This is a given single capitalist society, an economy governed by the laws of world capitalism, originating in the separation of the laborer from control over the means of production.
[…]
Capital, said Marx, is not a thing, but a social relation of production established through the instrumentality of things. The instrumentality which establishes this exploitive relationship is, as is well known, the means of production alienated from the direct producers, i.e., the proletariat, and oppressing them. The capitalist’s mastery over the worker is only the “mastery of dead over living labor”. The material manifestation of this greater preponderance of constant over variable capital is the preponderance in the production of means of production over means of consumption. In capitalist society it cannot be otherwise for the use values produced are not for consumption by workers or capitalists, but by capital, i.e., for productive consumption or expanded production. The greater part of the surplus value extracted from the workers goes back into this expanded production.
The Russian exploiters are so well aware of the fact that surplus value, in the aggregate, is uniquely determined by the difference between the value of the product and the value of labor power, that the Plan for 1941 stipulated openly that the workers are to get a mere 6.5 per cent rise in wages for every 12 per cent rise in labor productivity.
“This proportion between labor productivity and average wage”, brazenly proclaimed Voznessensky, “furnishes a basis for lowering production cost and increasing socialist (!) accumulation and constitutes the most important condition for the realization of a high rate of extended production.”
C.L.R. James:
Today this antithesis between production for use and production for surplus labor can be seen nowhere so clearly as in Stalinist Russia. And that stamps this society as being of the same inner essence as capitalism. Up to 1928, the use-value of the commodity predominated to the limited extent that this was possible in a backward society in the environment of the world market. The industrial proletariat in that year lived, at the very least, up to the standard of 1913. The first Five Year Plan predicted doubling of the subsistence of the working class by 1932.
But from 1929 a decisive change began. The lowering of agricultural prices in the world market threw the Russian plan into chaos. The competition on the world market, in its modern form of imperialist war, compelled the bureaucracy to reorganize the plan to meet the threat of Japan, at heavy cost; and with the coming to power of Hitler and his announcement that the main enemy was Russia, the change in Stalinist production and in Stalinist society became more uncontrollable. The bureaucracy was compelled to continue the process of industrialization at feverish speed. Under such circumstances, in a backward country, with an immature working class, the main aim of production inevitably must become the production of surplus labor, for the sake of more production, for the sake of still more production.
[…]
In all previous societies, land was the main factor in production. In capitalist society the main factor is accumulated labor, within the environment of the world market. If the laborer controls the accumulated labor we have socialism. Wherever it controls him we have capitalism. “It is only the dominion of past, accumulated, materialized labor over immediate living labor that stamps the accumulated labor with the character of Capital.” Marx repeatedly wrote these definitions.
Friedrich Engels:
But, the transformation — either into joint-stock companies and trusts, or into State-ownership — does not do away with the capitalistic nature of the productive forces. In the joint-stock companies and trusts, this is obvious. And the modern State, again, is only the organization that bourgeois society takes on in order to support the external conditions of the capitalist mode of production against the encroachments as well of the workers as of individual capitalists. The modern state, no matter what its form, is essentially a capitalist machine — the state of the capitalists, the ideal personification of the total national capital. The more it proceeds to the taking over of productive forces, the more does it actually become the national capitalist, the more citizens does it exploit. The workers remain wage-workers — proletarians. The capitalist relation is not done away with. It is, rather, brought to a head. But, brought to a head, it topples over. State-ownership of the productive forces is not the solution of the conflict, but concealed within it are the technical conditions that form the elements of that solution
Guy Debord:
The concentrated spectacle belongs essentially to bureaucratic capitalism, even though it may be imported as a technique of state power in mixed backward economies or, at certain moments of crisis, in advanced capitalism. In fact, bureaucratic property itself is concentrated in such a way that the individual bureaucrat relates to the ownership of the global economy only through an intermediary, the bureaucratic community, and only as a member of this community. Moreover, the production of commodities, less developed in bureaucratic capitalism, also takes on a concentrated form: the commodity the bureaucracy holds on to is the totality of social labor, and what it sells back to society is wholesale survival. The dictatorship of the bureaucratic economy cannot leave the exploited masses any significant margin of choice, since the bureaucracy itself has to choose everything and since any other external choice, whether it concern food or music, is already a choice to destroy the bureaucracy completely. This dictatorship must be accompanied by permanent violence. The imposed image of the good envelops in its spectacle the totality of what officially exists, and is usually concentrated in one man, who is the guarantee of totalitarian cohesion. Everyone must magically identify with this absolute celebrity or disappear. This celebrity is master of non-consumption, and the heroic image which gives an acceptable meaning to the absolute exploitation that primitive accumulation accelerated by terror really is. If every Chinese must learn Mao, and thus be Mao, it is because he can be nothing else. Wherever the concentrated spectacle rules, so does the police.
[…]
After Kronstadt, the bureaucracy–sole proprietor of a State Capitalism–consolidated its power internally by means of a temporary alliance with the peasantry (with the “new economic policy”) and externally by using workers regimented into the bureaucratic parties of the Third International as supports for Russian diplomacy, thus sabotaging the entire revolutionary movement and supporting bourgeois governments whose aid it needed in international politics (the power of the Kuonmintang in China in 1925-27, the Popular Front in Spain and in France, etc.). The bureaucratic society continued the consolidation by terrorizing the peasantry in order to implement the mast brutal primitive capitalist accumulation in history. The industrialization of the Stalin epoch revealed the reality behind the bureaucracy: the continuation of the power of the economy and the preservation of the essence of the market society commodity labor. The independent economy, which dominates society to the extent of reinstituting the class domination it needs for its own ends, is thus confirmed. Which is to say that the bourgeoisie created an autonomous power which, so long as its autonomy lasts, can even do without a bourgeoisie. The totalitarian bureaucracy is not “the last owning class in history” in the sense of Bruna Rizzi; it is only a substitute ruling class for the commodity economy. Capitalist private property in decline is replaced by a simplified, less diversified surrogate which is condensed as collective property of the bureaucratic class. This underdeveloped ruling class is the expression of economic underdevelopment, and has no perspective other than to overcome the retardation of this development in certain regions of the world. It was the workers’ party organized according to the bourgeois model of separation which furnished the hierarchical-statist cadre for this supplementary edition of a ruling class. While in one of Stalin’s prisons, Anton Ciliga observed that “technical questions of organization turned out to be social questions”(Lenin and the Revolution).