There was a national socialist worker's party in Germany and there was a fascist party in Italy. The use of "fascism" as an abstract term was pioneered by the communists in the Dimitrov thesis. They used the Italian party name to describe similar movements in across all of europe. To them it was a extreme ruling class reaction to the revolution in Russia aping some of the antics of the Bolsheviks. In WW2 it swept over to the mainstream discourse amongst the liberals in the West to describe the axis powers. Starting with the war you would also get non-marxist theories about what this «fascism» thing is about. That discourse is going on till this day.
source: Fascism: A Very Short Introduction by Kevin Passmore.
Passmore spends a lot of time to emphasizing the minute differences between the basis of the Romanian, German, Italian, Bulgarian, Hungarian and Spanish movements commonly grouped under this term.
hi! you may be interested in a couple of previous posts