The difference is bias. Chomsky is a syndicalist socialist and believes something isn't 'real socialism' if it is not directly owned by the workers and that state capitalism is when the state owns everything.
Rather than accepting the common view among U.S. economists that a spectrum exists between total state ownership of the economy and total private ownership, he instead suggests that a spectrum should be understood between total democratic control of the economy and total autocratic control (whether state or private). -Basic summary for description of Chomsky's belief towards private ownership from Chomsky: Language, Mind, Politics (second ed.) by James McGilvray
However, many different sources disagree with this definition. Cambridge English Dictionary defines state capitalism as a form of capitalism in which the government controls some property, resources, money, etc. and sources like Encyclopedia Britannica define capitalism as a system where "most means of production are privately owned and production is guided and income distributed largely through the operation of markets". Oxford's Lexicon defines capitalism as an economic and political system in which a country's trade and industry are controlled by private owners for profit, rather than by the state, so to them, Chomsky's definition would automatically describe a system other than capitalism. As I have explained previously, the Soviet Union under Stalin to 1991 followed a system of Marxist socialism known as dictatorship of the proletariat lower-stage communism. Basically, in his work Critique of the Gotha Program, Karl Marx mentions the dictatorship of the proletariat, a form of the state where members of the working class take control of the state and nationalize the means of production in order to make everything publicly owned and improve the standing of the current community.
Between capitalist and communist society there lies the period of the revolutionary transformation of the one into the other. Corresponding to this is also a political transition period in which the state can be nothing but the revolutionary dictatorship of the proletariat. -Karl Marx
This is the system the Soviet Union was following, where the state owns the means of production on behalf of the common worker, all property is public property under the state and can only be utilized by public servants (the same way that the White House in the United States is public property and can only be used by members of the Executive branch/ government officials who work with that branch), and personal property is given to members of the proletariat based on the principle of "each according to his contribution" (which in many socialist countries, meant the members of the state get the most personal property). Under Chomsky's definition, this version of socialism would be state capitalism and Karl Marx would have to be considered a state capitalist, which is ridiculous. Also, certain forms of market socialism would have to be seen as capitalism and not 'real socialism':
"It is an economic system that combines social ownership of capital with market allocation of capital...The state owns the means of production, and returns accrue to society at large." -Paul R Gregory describing market socialism, Comparing Economic Systems in the Twenty-First Century
Chomsky even once stated that countries in Western Europe were 'more socialist' than the USSR, which would make no sense especially considering that the Index of Economic Freedom, an index created by The Wall Street Journal and The Heritage Foundation think tank to rank how capitalist a nation is based on criteria like legal protection of private property rights & private business freedom, ranks many Western European nations as some of the most capitalist and economically free. Nations in the top thirty of this index include 'socialist' nations like Germany, Iceland, Luxembourg, Austria, Ireland, Switzerland, the Netherlands, Denmark, and the United Kingdom. This clearly shows Chomsky's bias against Marxist socialism, especially since Marxist socialists like David McNally see Marxist socialism as incompatible with market economics based on the writings of Karl Marx, so to them, every Western European nation could never truly be seen as socialist.
Now to Chomsky's credit, the USSR was briefly capitalist from 1921 to 1928 under the New Economic Policy which implemented a market based economy with private ownership. However, the policy was undone in 1928 and the USSR returned to a command economy and the dictatorship of the proletariat model. After that, private property was pretty much non-existent in the USSR with the state controlling the means of production on behalf of the common worker (which is pretty much how Oxford defines state socialism: A political system in which the state has control of industries and services.)
Basically, Chomsky's socialism is a form of syndicalism where there is no state and labor unions own the means of production, with anything else being capitalism. Soviet socialism, meanwhile, is Marxist state socialism that believes the state owns the means of production on behalf of the common worker under a command economy and advance into the final stage of communism.