Of course, it’s better to refer to them as Fascists – that’s the more accurate term that fully refers to both of those groups

Yes, you’re right, although on the other hand Nazism and classical fascism are also pretty different despite some surface level similarities. Even the fascist movements at the time struggled to figure out a unified position on racism/anti-semitism, corporatism and state structure.

If you want a few kicks, read what ᴉuᴉʅossnW thought of Hitler before he was pressured into saying nice things closer to WWII. My favorites are “silly little monkey” and “A mad little clown”. He was surely regretting their alliance long before he was hanged.