To be fair, the NsDAP (National socialist German Workers' Party) was founded in 1920 and the PNF (National Fascist Party) in 1921, therefore there does not appear to be a deliberate choice to put distance between them and a preexistent movement. It is also wrong to assume that the Nazi's antisemitism was a spin on Italian Fascism.

As Kershaw points out, Hitler's antisemitism was an integral part of his personal and political beliefs since the years immediately following WW1 and likely dated back to the years of the war themselves. It also was quite widespread among other prominent figures of the NsDAP.

You are correct though in pointing out that antisemitism and racism were not original features of Italiam Fascism. This is particularly relevant because the understanding of history and international politics in terms of racial struggle was a definitive character of Hitler's personality.

A set of simple, almost brutal beliefs ended up shaping not only Hitler's personality but also his political action and his concept of the party and the state. In addition to the aforementioned antisemitism and simplistic view of history, his radical refusal of beurocracy in favour of a sort of personal committment to the leader - the working towards the fuhrer led to the peculiar configuration of Nazi government, shaped by competing spheres of influence, and the phenomenon of cumulative radicalization which explains why many of the more extreme istances emerged without an explicit imprimatur by Hitler.

On the other hand Mussolini held a strong confidence in the traditional role of beurocratic structures - in this regard his admiration for Napoleon and personal inclination towards micromanaging played a role - and took many steps to replace wherever possible the preexisting structures of the Italian Kingdom with ones directly controlled by him, thus undermining the traditional powers' support. He was not completely successful, given that the King retained the almost absolute loyalty of the army and the Pope exerted a much stronger influence within italian society than he did in Germany. Italian fascism ended up therefore with two beurocracies working in a parallel way - or sometimes contented itself with putting black shirts on the old officies - which explains why in 1943 the Fascist Party could disappear so rapidly (the competing, traditional structures of the conservative state had not been dismantled).

While the Italian Army ha the King and the italian catholics had the Pope, the German Army was lacking a figure to rally behind. Many high officers went along according with the idea that they should not mettle with political problems; therefore the "opposition" to Hitler was born without a head, while the italian conservatives unwilling to align with Fascism had one (albeit unenthusiastic) or even two from the start. The german church opposed, at times, the Nazi regime but had to play a lot safer given the relative stranghts of the parts involved.

Do not the sweraring of loyalty to the leader, common to both countries, mislead you. While this was the result of Hitler's true personal beliefs (appearing as well in his refusal to give a beurocratic structure to the party itself), it was mostly opportunistic and propagandistic for Mussolini as a way to put himself on the same formal level with the king.

Also in foreign politics, Mussolini enjoyed the idea of using Italy's decisive weight to gain power within a context of unstable equilibrium in times of peace, up until the dissolution of Czechoslovakia. On the other hand Hitler's policy was oriented towards a breaking of the equilibrium, constantly overplaying his hand and rapidly growing overconfident in his own strenght and political acumen. It's not that Mussolini wanted peace, but his behaviour followed a - sometimes careless - spin on italian traditional policy of giri di valzer in refusing a strong committment to a single partner, at least until the general deterioration of the european situation and his own blunders forced him to cast his lot with Germany.

Hitler's foreing policy was instead something completely new, almost entirely out of the influence of the professionals and apparently quite puzzling for the british and french foreing offices, in his continuous oscillation between "genuine" offers of pacification, and threats of unrelenting war.

 

In short, I would not put much thought on the efforts by both the Fascist and the Nazies parties to present themeselves in a certain way, given the almost entirely propagandistic nature of these efforts.

Rather the two regimes had many significative differences, steming both from the preexisting structures of the two countries (presence-absence of a King, stronger influence of the church) and the personal influx of the leaders (personal loyalty versus beurocracy, racial struggle versus political realism, etc.)

 

In pointing out the differences I glossed over a significant number of points of contact (I need to mention here the extremely weak democratic traditions of both countries); still the two regimes appear remarkably different. I also skipped the economic part which is not my strongest point and required long treatment.

As sources the main ones are De Felice's biography of Mussolini and Kershaw's biography of Hitler.

I have gone previously into the relation between Nazism and Fascism here where I detail how in some ways the Nazis were inspired by Italian Fascism.

I think /u/Klesk_vs_Xaero has covered some of the most important points. Playing off of their excellent response, I hope it is ok if I go into a bit more detail regarding some of the structural differences.

Taking the differences in foreign policy and general approach to how the world was viewed described below/above, this difference in approach had wide reaching economic and structural consequences. For Mussolini's fascist regime war can best be described as a tool to enhance power, which is in a sort of way the classical European imperialist approach. War in Ethiopia to build a colonial empire, war in Greece to extend one's political influence over said country.

For the Nazi regime, war was a raison d'etre, something that was as inevitable as it was good and necessary. Especially the war in the East, against the Soviet Union and Poland and the subsequent occupation was understood by the Nazis not just as "the extension of politics by other means" as Clausewitz would say but rather the method to not only improve one's own racial community but also to gain the living space necessary and to annihilate what they regarded to be the most important tool of the Jewish conspiracy: Socialism and Communism. Approaching the world with the understanding that at its center was the massive struggle between Jews and Germans, they viewed the abolishion of private property, Communism as an international ideology and by extension the Soviet Union as tools of said conspiracy needing to be destroyed.

This was very clear from the beginning and while Italian fascism certainly was an anti-Communist movement too, they were rather contempt with eliminating it from Italy as a political force. The Nazi regime from its very beginning geared up for war. By 1936, the Nazi regime with the voluntary participation of the capitalist class had completely redesigned Germany's economic system towards war. In the Four Year Plan agency, every industry had their own council where the leaders of the biggest firms worked together to plan the total mobilization of the German economy geared towards war with the unwavering financial support of the Nazi government.

Now, fascist Italy had a corporatism phase too in the 1920s but not with the goal of mobilizing the whole economy in the service of a war that was to be fought in 4-5 years. And while both regimes aimed for economic autarky, the Nazis could at least up to 1943/44 deliver the huge profits it had promised the German Capitalist Class while Fascist Italy, which tried a more "classical" imperialist approach with its colonial war in Ethiopia, failed to deliver.

While these superficial similarities have lead some critics contemporary to Nazism and Italian fascism to conclude, that they were both forms of the same phenomenon, European fascism, it is not as easy as that. While we certainly can attest some historical similarities on an ideological level -- anti-Communism, extreme nationalism, xenophobia, affinities to corporatism and so on -- the important difference that influenced the what structures were formed how lies in the fact that the Nazis approached the world as a conflict that needed to be fought between the German and the Jewish race and that at its core lay the principles of race and space. The Italian fascist regime on the other hand did not fully ascribe itself to such a völkisch view of the world but is really more in line with extreme right wing European Imperialism of the time.

Sources:

• Adam Tooze: The Wages of Destruction.

• Robert Paxton: The Anatomy of Fascism (2004).

• Lorna Waddington: Hitler's Crusade: Bolshevism and the Myth of the International Jewish Conspiracy, 2007.

The great difference between fascism and national socialism is already hinted at in the name. "Fascis" were the symbol of state-might in Ancient Rome. The fascists therefore based their whole state-system on ancient Rome. The new Italy as a fascist country was legitimized as a descendant of roman greatness, which to achieve was its ultimate goal.

This was not the case in Germany and with the NSDAP. This party based its legitimacy on the people, not a past area. The national socialists did not want to go back to some ideal of past times, but to create something wholly new. They did not want to secure old boarders, create old state-structures, but wanted to create a whole new Reich as the perfect state for the German people with new boarders, organizations and ideas.

The fascists had an ideal which they looked up to: Rome The national socialists wanted the Volksgemeinschaft. Their ideal was not the state. A state was just a necessary means to control the people. Their goal was a real and true Volksgemeinschaft, a community of same-blooded and minded people so strong and tight, that it became a whole new entity. Italian fascism never had such a goal in this strictness.