Which of these is a difference between nazisum and fascism?

Fascism: The original Fascists were a breakaway faction that disagreed with the Italian Socialist Party about World War I. Benito Mussolini (an influential Socialist leader and writer) and his followers believed that World War I was a great opportunity to unite the people of Italy and take land from Austria that they thought rightfully belonged to Italy. The Socialist Party stood against Italian involvement in the war, as most Socialists and Communists of the time did.

As the War ended and Italy won less Austrian territory than expected, Mussolini's breakaway faction began its rise to power. Their new Fascist Party (named after the "fasces", a symbol used to show the ranks of government officials in the Roman Republic/Empire) emphasized militarism, extreme nationalism, authoritarianism and a general "might makes right" philosophy. They opposed both Communist and Capitalist economics, preferring instead their own form of economy called "Corporatism", where the government breaks the economy into smaller pieces, each controlled by a joint government and private management.

National Socialism, or, more commonly, Nazism: is a sort of political philosophy that pretty closely resembles Fascism. It arose from small extreme right-wing and anti-semitic political parties in Germany after World War I. First and foremost, Nazism emphasized racism, especially anti-semitism. Like Fascism, it also emphasizes militarism, extreme nationalism (although in Nazism's case, "nationalism" is based on races, not countries- "Germans are good, Jews are bad"), authoritarianism, and "might makes right". They twisted existing ideas like Darwinism into new, messed-up ideas, like that it was perfectly OK to wipe out other races because "obviously" German people were better than other people.

Adolf Hitler, the primary leader of Nazism, fully admitted that he didn't care too much about economics, but when the Nazis ruled Germany, their economy largely remained capitalist- although Jews were removed from it, and the Nazis would occasionally take control of businesses and companies when it was convenient for their goals. While Hitler and his Nazi Party were trying to come to power in the 1920's, they did say a lot of things to make themselves sound like they were Socialists- but in reality, they were quietly promising big business owners that it wasn't the case, and once they came to power, they proved it.

The overwhelmingly major difference between the two, as you may have noticed, is race. Nazism was profoundly racist; Fascism was not. Mussolini even criticized Hitler's "pointless racism", and appears to have initially believed Hitler to be a buffoon (and he was not the only person to make that mistake). Only once Hitler's Germany became very powerful and Italy needed allies (they were trying to conquer smaller countries like Albania), did Mussolini join Hitler's side. After World War II started and Italy's military showed itslef to be fairly weak, Germany began to push its lesser partner to adopt racist laws similar to the ones the Nazis had; Italy did so, so by the time the war was coming to an end, Fascist Italy did very closely resemble Nazi Germany.