The Soviet Union nationalized all industry. There were no privately owned businesses.
The "socialist" Nazis didn't nationalize industry. They even sold off state industry to the private sector. What the Nazis did have was a war economy, with the private sector drafted into building war materiel.
In that respect they resembled another major power whose private sector was drafted into building war machinery, the United States. And von Mises noted that similarity.
https://oll.libertyfund.org/quote/mises-on-how-price-controls-lead-to-socialism-1944
It is sometimes difficult for modern readers to imagine how much government intervention in the economy took place during World War Two, even in the so-called liberal democracies like Great Britain and the United States. It would take a refugee from Nazi Europe, such as the economist Ludwig von Mises, to see the close parallels between the economic policies of Nazi Germany and the United States of President Roosevelt. These parallels arose because both economies faced similar difficulties in time of war.
With international free trade disrupted, goods with multiple uses (such as gasoline and rubber) had to be allocated away from consumer goods production to war goods production such as tanks and aircraft. Since the government did not wish to pay more for these goods in a free market, thus competing with consumers for the use of these goods, it used regulations and controls like rationing to take the bulk of these products for its war industries and to ration what was left to the consumers.
What the Nazis did was a de facto nationalization, but not a de jure one. Nonetheless, the economy was controlled by the government. They maintained the fiction of private property while in fact taking complete control themselves and making all the decisions.
They were different types of socialism, but they were both socialist. Which was Mises's point, and the point of the large number of links I provided. There is no question that what they had in Germany and Italy were socialist regimes.
https://www.americanthinker.com/articles/2007/11/the_nazis_were_maxists.html
“The Nazis were Marxists, no matter what our tainted academia and corrupt media wishes us to believe. Nazis, Bolsheviks, the Ku Klux Klan, Maoists, radical Islam and Facists — all are on the Left, something that should be increasingly apparent to decent, honorable people in our times. The Big Lie which places Nazis on some mythical Far Right was created specifically so that there would be a bogeyman manacled on the wrists of those who wish us to move “too far” in the direction of Ronald Reagan or Barry Goldwater.
“The truth about the Nazis was that they were the antithesis of Reagan and Goldwater. Let us consider the original Nazi movement and its evolution. The National Socialist movement began in Austria with Walter Riehl, Rudolf Jung and Hans Knirsch, who were, as M.W. Fodor relates in his book South of Hitler, the three men who founded the National Socialist Party in Austria, and hence indirectly in Germany. In November, 1910, these men launched what they called the Deutschsoziale Arbeiterpartei. That party was successful politically. It established its program at Inglau in 1914.
“What was this program? It was against social and political reaction, for the working class, against the church and against the capitalist classes. This party eventually adopted the name Deutsche Nationalsozialistche Arbeiter Partei, which, except for the order of the words, is the same name as “Nazi.” In May 1918, the German National Socialist Workers Party selected the Harkendruez, or swastika, as its symbol. Both Hitler and Anton Drexler, the nominal founder of the Nazi Party, corresponded with this earlier, anti-capitalistic and anti-church party.
“Hitler, before the First World War, was highly sympathetic to socialism. Emile Lorimer, in his 1939 book, What Hitler Wants, writes about Hitler during these Vienna years that Hitler already had felt great sympathy for the trade unions and antipathy toward employers. He attended sessions of the Austrian Parliament. Hitler was not, as many have portrayed him, a political neophyte in 1914.
“The very term “National Socialist” was not invented by Hitler nor was it unique to Germany. Eduard Benes, President of Czechoslovakia at the time of the Munich Conference, was a leader of the Czechoslovak National Socialist Party. Ironically, at the time of the Munich Conference, out of the fourteen political parties in the Snemovna (the lower chamber of the Czechoslovakian legislature) the party most opposed to Hitler was the Czechoslovak National Socialist Party. The Fascist Party in Czechoslovakia was also anti-Nazi.
“The first and only platform of the National Socialist German Workers Party called for very Leftist economic policies. Among other things, this platform called for the death penalty for war profiteering, the confiscation of all income unearned by work, the acquisition of a controlling interest by the people in all big business organizations and so on. Otto Strasser, the brother and fellow Nazi of Gregor Strasser, who was the second leading Nazi for much of the Nazi Party’s existence, in his 1940 book, Hitler and I revealed his ideology before he found a home in the Nazi Party. In his own words Otto Strasser wrote: “I was a young student of law and economics, a Left Wing student leader.”
“Consider the following text from that platform adopted in Munich on February 20, 1920 and ask yourself whether it sounds like the notional Right or the very real Left:
“We ask that the government undertake the obligation above all of providing citizens with adequate opportunity for employment and earning a living. The activities of the individual must not be allowed to clash with the interests of the community, but must take place within its confines and be for the good of all. Therefore, we demand an end to the power of the financial interests. We demand profit sharing in big business. We demand a broad extension of care for the aged. The government must undertake the improvement of public health.”
In his 1939 indictment of Nazism, Germany Rampant, Hambloch has an entire chapter on political parties under the German Empire before the First World War and political parties under the Weimar Republic. Hambloch lists parts of the “Left,” “Right” and “Centre” in the German Empire pre-1914, but there are no “Left,” “Right” or “Centre” parties in the Weimar Republic, but rather “Weimar Parties, i.e. those who supported the republican constitution,” “National Reactionary Parties” and “Revolutionary Parties.” The Nazis are listed, along with the Communist Party of Germany, as the two “Revolutionary Parties.” Pointedly, the Nazis were not considered a “National Reactionary Party.”
Consider these remarks of Nazi leaders. Hitler on May 1, 1927:
“We are socialists. We are enemies of today’s capitalistic system for the exploitation of the economically weak, with its unfair salaries, with its unseemly evaluation of a human being according to wealth and property instead of responsibility and performance, and we are determined to destroy this system under all conditions.”