In order to understand socialism, it's perhaps useful to understand where it came from. Broadly, Western economies went from Feudalism through the sort of proto-capitalism of mercantilism to capitalism. These were deeply class-based systems where the bottom rung were disempowered, exploited and wasted. Effectively, serfdom was slavery in feudalism, and in capitalism wage slavery was barely any improvement; in both cases the elites - aristocrats then capitalists - ran the affairs of their state and took disproportionate quantities of economic production for themselves. An idea of capitalism was that it was supposed to enrich, develop and empower the poor. The realisation of the 19th century was that it didn't appear to do so, it just transferred power and wealth to different masters. Marx was around to see deskilling, where the average education and capabilities of the poor declined, because working in a factory doing menial tasks meant they no longer needed to do things like read or write so increasingly didn't even learn. Inherent to ideas of socialism were therefore to finally achieve the raising of the poor where capitalism had failed: things like egalitarianism, reduction and removal of class, to an extent freedom (of all, but particularly the poor) to exercise control over their own lives.
The aim of socialism is about seeing that the poor achieve economic security and opportunities - to develop, thrive, grow. Socialists reasoned that that could only be guaranteed when the workers owned the means of production, because otherwise the profits would always be taken by the small cliques who did own, and then marginalise the workers. And that's why socialism is generally termed as ownership of the means of production by the workers.
Taking this basic sort of idea, if we then look at Nazi Germany's economy, what did it do? Actually, it utterly disempowered the poor politically as they were ruled by a self-appointed party elite who had no particular interest in them. They couldn't even bargain with their bosses any more for instance: labour unions were scrapped and replaced by state labour organisations. The Nazi Party entrenched their class position, and uths the class advantages of the middle and elites. It ensured private ownership such that the profits of business still surged to the capitalist bosses, who were now firmly in cahoots with the ruling party.
We could contrast this with the USSR: whilst also run by a single party that was dictatorial and disconnected from the populace, that party was ideologically and - to a substantial extent still in practice - a party representing the workers, who worked their way up teh greasy pole. And the USSR really did hugely diminish class - the poorest could achieve and rise in ways they would struggle to do far more in the West, without the same barriers of wealth, status and snobbery in their way. For all the terrible flaws of either, you can really see where the USSR was aiming at in terms of socialist ideals, where Naziism couldn't have given a hoot. The Nazi Party just wanted enough bread and circuses to keep the working classes pacified: it didn't want them empowered, active, and seeking claims on economic production the Nazis didn't believe they deserved.
"Economic control" is thus not really meaningful in socialist terms if it doesn't serve the interests of the masses, and in Nazi Germany, it didn't. Nazi economic control served the objectives of the Nazi Party and their nationalist fantasies, and as a byproduct the economic elites who agreed to work as their partners, who still owned and reaped the profits.
