Nazism was just a racist version of fascism.one off-topic reply to answer the question as to the difference, simply in a way anyone can understand without alot of reading and only a basic understanding of metaphor.
Fascism is Corporate state, the whole of society working together as a single body.
Nazism is racial state, the exclusion of one section of society from the body in order the raise the rest.
Authoritarian leftists like me may lament the fact that nazism basically means that all modern authoritarian parties are racist, but that's the way it is.
But I won't disagree that Mussolini had little time for hitler's racial policy, let alone what Franco thought of them.