It's a bit cliche, but I'll trot out the most well accredited definition of Fascism in recent years - coming from Robert Paxton's Anatomy of Fascism:
"Fascism may be defined as a form of political behavior marked by obsessive preoccupation with community decline, humiliation, or victim-hood and by compensatory cults of unity, energy, and purity, in which a mass-based party of committed nationalist militants, working in uneasy but effective collaboration with traditional elites, abandons democratic liberties and pursues with redemptive violence and without ethical or legal restraints goals of internal cleansing and external expansion."
Ian Kershaw and co. also constitutes an important facet in the study of the Nazi German state as (quoting from Wikipedia for the sake of brevity):
"[...] the Nazi dictatorship was not a totalitarian monolith, but rather an unstable coalition of several blocs in a "power cartel" comprising the NSDAP, big business, the German state bureaucracy, the Army and SS/police agencies (and moreover, each of the "power blocs" in turn were divided into several factions). In Kershaw's opinion, the more "radical" blocs such as the SS/police and the Nazi Party gained increasing ascendancy over the other blocs after the 1936 economic crisis, and from then onwards increased their power at the expense of the other blocs."
Fascism tends to manifest itself in uneasy coalitions of many bases of power working together, generally with the tension of a grassroots based "street-movement" (Squadrismo, Sturmabteilung, etc.) with factions of big business and conservative/militarist government. There's another discussion to be had on the social-revolutionary elements of the grassroots parties and continuation of the "redemptive violence" on the street level that becomes an embarrassment to the parliamentary fascists (one which I find intensely interesting), but it's only tangentially related here. The fact of the matter is that fascist governments have historically gone through a variety of transitory phases where, as Kershaw and Mommsen write, the regimes either moderate or go through a process of cumulative radicalization. Mussolini's economic policies in 1923 look entirely different from 1938 which looks entirely different from 1944, and this can all be seen easily through the rhetoric. For instance, Mussolini's rhetoric on social-revolutionary aspects were toned down hard during the crackdown of "excessive" Squadristi violence in the mid 1920's to reassure the King and his business associates that they were not revolutionary, but when they abandoned him for the Allies, the Social Republic once again brought it to the fore of their propaganda because it was convenient as a tool to demonize the enemies of Mussolini. Hitler too - the term privatization was coined to describe Germany dismantling the public sector after the rise to Nazi rule and the business allies for Germany were huge. They then went on and off when intervening in the economy until, by the end of the war, economic intervention was quite high as a result. The Nazis also were forced to embark on some restrictions of business such as price controls to appease the working class supporters of the NSDAP because, after all, much of early Nazi policy can be characterized by an intense fear of losing their hold on Germany's working class and being seen as just another bourgeois party. Essentially, you cannot classify any fascism as wholly "capitalism" or "socialism", because the big fascisms we saw were very beholden to their political and economic circumstances. Fascism, if anything, is supremely adaptable and we saw changes in policy and rhetoric both towards and away from the free market depending on whatever was "good" for the Volksgemeinschaft...
Related to this discussion is viewing Nazism distinctly through the lens of anti-intellectualism and the German concept of the weltanschauung or worldview. This emphasizes not so much principles and theories, but simply the act of doing in the interest of the nation. Fascist policy therefore, as I stated, was driven by expediencies and circumstances, not by any codified plan or theory for state or economy. This can especially be seen by how Germany was run, mostly as a series of faction against faction and bureaucracy and bureaucracy in a Hobbesian "war of all against all" where the whims of the Führer was decisive. Describing Nazi economic policy as socialist, or command, or statist or what have you ignores the fact that it was above all an ad-hoc and chaotic system where policy was shaped by whoever had the Führers ear and the means to carry it out. Describing it as socialist implies there was some sort of plan, vision, or even principle behind it - but any comprehensive study on the fascist state in Germany will tell you literally none of this existed. You are projecting our views of economy and politics, and a sense of overall coherence, backwards to a historical moment where it did not exist. The idea that Nazi Germany was a totalitarian monolithic state that sought more and more control over both society and economy and was completely independent of any outside influence/did not have coalitions and interests to tend to is a trope at this point and its best to do away with that analysis of fascism. I personally find Arendt's Totalitarian Model pretty outdated both in discussions of fascism and communism and gladly a fair amount of historians agree with this sentiment.