What is the difference between socialism and nazism?

The German Nazi (National Socialist) Party was politically fascist, which is a corporatist, racist, overwhelmingly petty bourgeois pastiche of ideologies based on the supremacy of the state over the individual, the importance of tightly centralized power and the fetishization of national myths and heroes. Socialism is multinational and working-class in character, seeking to establish a fully democratic, classless society.

Confusion between, and the conflation of, Nazis and socialists is due to the Nazi Party's name, which was in full the National Socialist German Workers Party (NSDAP). When Hitler joined the DAP in the early 1920s and quickly became its most prominent member and leader, the party's basic politics were not much different from those that later marked the Nazis' rise to power -- anti-Semitic, anti-socialist, anti-communist, opportunistic and wedded to violence -- but they were murky. The party was also quite small, one of dozens of right-wing populist formations at the time. By upping the nationalist ante, scapegoating national minorities and adding "socialist" to the party's name, Hitler found he was better able to attract disenchanted WWI veterans and workers left jobless during the hard economic times that followed the Treaty of Versailles. To better distinguish his party and its ethos from the more established socialist and communist entities at the time, and to reflect its intense nationalism, he also added "national" to the name.

Socialism was the Nazis' greatest threat to power. In the years before the fated election that led to Hitler becoming chancellor, the Nazis' SA brownshirts engaged in incredibly violent, sometimes deadly, attacks on socialists and communists, in addition to their favored Jewish targets. Socialists and communists were some of the first concentration camp inmates.

ANOTHER PERSPECTIVE! It's true, the Nazi's hated other flavors of Socialism, Communism and probably any other imaginable method of collectivism.

But the Nazi version of Socialism is far more similar to traditional other forms of collectivism than it is to market economy.

Let's face it, collectivism feeds on big, controlling government; a market economy needs far less oversight and control.

You need a lot of government employees to round up a few million Jews and force them to their deaths.

Part of the problem here is, in addition to what was stated above about "Socialist" being part of the full name of the party, is the mistaken belief, primarily among Americans, that "big government" is the exclusively the purview of leftist, especially socialist or communist, political parties or systems. This is simply not true. Not all leftist movements advocate having large government apparatuses; for example, the various anarchist movements are typically considered extreme leftist yet advocate for small, localized governments at most. Even Communism, as described by Marx, advocates ridding of government in favor of local councils- Marx pointed to the Paris Commune as the prime example to follow.

By the same token, Fascism (including Nazism, which is different but similar enough to be lumped with it), is almost universally considered "extreme right" yet advocates for a powerful central government. Not to bring about a "workers paradise" as the Communists and Socialists would advocate, but to enforce their extremist nationalism and anti-communism. The sectors of government they enlarged most tend to be ones that conservatives tend to be accepting of, like the military, police, and counter-intelligence agencies. Fascist states also tended to be very friendly towards large corporations in their countries, and even worked hand-in-hand with them.

Instead of focusing on trivialities like the name or misconceptions of "big government", look at what the movements and parties actually advocate for, and, more importantly, what they actually do once they're in power. The Nazis forced concepts upon their people that are typical of the far right- extreme nationalism/patriotism, hatred of "foreigners" (in their case, mainly Jews but also Slavs- that is, Russians, Polish, Serbs, etc), desire for a return of a prior golden age (aka "make our country great again"), adulation for the military and military victories, and generally upholding capitalist principles (the Nazis largely practiced what we'd today call "crony capitalism"). Adolf Hitler even relaxed gun laws in 1938 for Germans (and restricted them for "foreigners")!