Fascism found its roots in Italy where it flourished in 1919, soon after World War One. On the other hand, Nazism, a German ideology, became popular in 1933.
Fascism originally referred to the ideological beliefs of fascists of Italy, who were mainly led by Benito Mussolini, the Italian dictator who came in power soon after the First World War and stayed in office until the end of Second World War. Nazism, also known as National Socialism, was the ideological belief of all those affiliated with the German Nazi party during the reign of Adolf Hitler, Fuhrer of Germany from 1933 to 1945.
Fascism aimed at combining or merging all elements in a society to eventually form an ‘Organic State’. For fascists, state welfare was the most important thing and all else was meaningless when compared to the integrity and sovereignty of the state. Nationalism, corporatism, totalitarianism and militarism were the ruling beliefs of Fascism. Nazism was pretty much similar to Fascism in this regard but Nazism focused more on the superiority of a single race (Aryan race) rather than welfare of the state as a whole. This is why it is a common belief that Nazism was more of a racial hatred ideology.
While class based society was considered to be an enemy in Nazism, Fascism allowed for the preservation of such a society.
For the Nazis, state was a means to advance the master race whereas for Italian Fascists, state was just another form of nationalism.
Then there is the difference between the origin and historical development of the words Fascism and Nazism. Fascism was derived from a Latin word fasces (a bundle of rods tied around an axe). Nazism or Nazi was derived by combining the first two syllables of Nationalsozialistische Deutsche Arbeiterpartei, Hiltler’s political party.