I have previously answered this question before here

the gist of it is, that while the Nazis never referred to themselves as explicitly fascist, they tended to stress the similarities of the movements; something that was picked up upon by leftist critics and theoreticians contemporary to the formative years of the two movements.

I think Hitler personally credited Mussolini with a lot when it came to inspiration, but the vast majority of Germans associated the word "Fascist" with "Italian". Nazism was explicitly billed as a German ideology, specific to Germany and not for foreign consumption. So while Fascism was seen as something of an ideological cousin, perhaps, it was not taken as the same thing. We could argue about Nazism being a subset of fascism from an outsider's perspective, but the Germans themselves saw it as something perhaps "related" but completely different, on an equal plane.

An interesting story here: after the battle of Berlin, a Hitler Youth soldier wakes up in a Soviet hospital. The Russian nurse asks him if he is a "fascist". He says no. You'd think he'd say no in any case for obvious reasons, but he literally was telling the truth as he saw it, because he thought she was basically asking if he was Italian. He was actually somewhat offended at the idea given the near universal German contempt for their "allies" by this stage of the war.