National Socialism is a TYPE of Fascism, but Fascism is not National Socialism. There's a lot of subtle but important differences.
This is something a lot of people forget.
How about Brazilian Integralism? That was Fascism that was (shock!) not racist!
Ehhhhh. It's racist, it's just not racist in the traditional sense. Their whole schtick was that Brazilians were a sort of Master Race because they believed due to the extensive mixing that occurred, they combined all the supposed "best traits" of the worlds' races. A sort of racism that works from the opposite end of the spectrum, the notion that "racial purity" is inferior to a "thorough mixing".
Mussolini's Fascism wasn't particularly anti-Semitic, though he would occasionally burn some Jews to keep Hitler off his back.
Eh. While by no means as proactive regarding intolerance and violence against Jews, they were not at all hesitant to hand over their Jews to the Nazis, knowing full well that meant either instant death, being worked to death, or being experimented on until death.
He also was far more socialist in his rhetoric (ironically).
How is it ironic? The entire point of Fascism was that it posited a "Third Way" between Capitalism and Socialism. Retaining notions of a privatized economy so long as the companies were willing to put the Fatherland before profits.
Franco? His Falangists were basically Mussolini-style Fascists to my understanding, but mi Caudillo himself was more of an old-school monarchist (something Hitler hated) with staunch support for the Catholic Church.
...as he should of, considering Franco
wasn't a Falangist, or rather, he was by no means an "authentic" Falangist. The opposite of what happened in Germany happened in Spain. Rather than the Traditionalist-Conservative parties and people being co-opted and radicalized into Fascist-National Socialism, the Fascists were greatly moderated by the Traditionalists and Conservatives. Really, what happened to the Falange is what von Papen, Hindenburg and so on was
hoping would happen to the Nazis. They were banking on Hitler either being "reined in" by the responsibilities of governing or failing that, Goering(by far one of the most reasonable and level-headed of the Nazis) being able to wrestle control of the NSDAP from Hitler.
So yeah, you've got very different types of Fascism, and National Socialism is just one. The worst one.
Fascism runs the spectrum of barely-fascist, generic military-authoritarian(your Francos, Horthies, Jozef Tisos) to the absolutely insane, balls-out madness(Himmlers, the Ustase, the Iron Guard).
The Ustase in particular are notable, some of the **** they were doing made
Himmler and the SS tell them to tone it the **** down.