Hitler's definition of a 'socialist':
Ian Kersahaw wrote the following in his book, Hitler: A Biography
Hitler explicitly and vehemently rejected the Marxian notion of class struggle. In regards to capital, as early as 1920, he made a distinction between financial capital and industrial capital, disapproving of the former and approving of the latter. He did, however, advocate for the solving of the "social question", as it was termed in that period. Essentially, he was a statist and implemented some things we would consider "social democratic", but without the democratic parts, and expropriated and nationalized property and assets on an ad-hoc basis, but not particularly along any specific ideological program.
Nazi economics was about infrastructure and rearmament, state directed but operated by large existing entities, but also, and this often gets ignored, as it is a paradox, for a movement that wanted autarky as its end goal, it sure went out of its way to foster more European economic integration with states in Central and Eastern Europe, both before and after the war began.
Private property was protected (up to a point, of course), but prices, wages, and perhaps most important politically, interest rates from financial institutions, were subject to regulatory intrusion from the state. Hitler was certainly a collectivist and a statist who used the power of the state to redistribute resources, but he was not a dialectic materialist, and his notion of the term socialism was that Marx had corrupted it from its Aryan roots.
It should be noted, however, that the approach taken was of protecting private property while looking to expand the role of the state in the provision of benefits and using the state to jumpstart infrastructure projects to strike at unemployment was not that radically different from the SPD's approach in government. The difference of course comes in two strands: one, the SPD was far more friendly to the idea of independent trade unions, and two, the NSDAP brought in a cavalcade of anti-usury measures in the banking sector in 1933 (Hitler's initial speech as Chancellor even makes note of usurious interest rates, a relatively strange topic for the kind of speech he was making) and used state force to settle the issue of Depression era depositor losses. These difference of course make sense when you consider the parties in question, as the SPD rose from the trade union movement, after all, and the NSDAP believed international finance and banking in general to be a Jewish plot, so they had no issues telling lenders to take a hair cut en masse.
It would be incorrect to call Hitler a socialist in the Marxian sense of the term. It would also be incorrect to call Hitler any conventional economic label we use today (like "social marketeer" or "state capitalist").
If there is one parallel I can come up with, it would be the Russian economy under Putin since 2011, in which rule of law is so far gone that it is well known that the state wields ultimate power when it chooses to, but it only chooses to sparingly, because the economy isn't the focus of the political project.
The thing about Nazi ideology is that it was always opaque on questions relatable to contemporary countries because, much like Kevin from the Office who used a made up number to balance the books, the Nazis used Jewish perfidy to fill in the gaps.