Assuming you mean as description of a contemporary person, in casual sense.

A nazi is someone consciously inspired by Nazi Germany, typically by using its symbolism or alluding to it, holding some ideas specific to the period but not necessarily all. A fascist is someone that supports a specific model of government and policies derived from ideology called fascism.

I feel like each answer here is wrong and right.

Literally, Nazi was a shortened version of National Socialist, and was the anglicized name for the German party that Adolf Hitler rose to power in.

In the vernacular, Nazi is a somewhat catch all to describe various fractions and identified ideologies which the broad usage I think hurts discourse.

Some people mean in this general way, any racist, or ethnostate advocate could be considered a Nazi, as could any racist or fascist group.

I’m not for any of it, but the fluidity of usage ends up feeling like hyperbole when someone is not a literal Nazi, or doesn’t even share Nazi values and beliefs.

When describing our enemies, I think static definition matters, because inaccuracies can be an attack surface to dismantle arguments.

Nazi refers to the German Nazi party, while “fascist” refers to broad reactionary movements usually found in decaying Capitalist countries as a safeguard against rising Socialist or Communist sympathies among the Working Class, with its own unique set of aspects like ethno-centrism, xenophobia, intense millitarization, etc.

I understand all Nazis are fascists, but not all fascists are Nazis

Aesthetic mainly. The are both manifestations of the same decay of capitalism.

It usually doesn’t matter

If you read Mein Kampf it’s really focused on “the Jews”.

Nazism was about anti-semitism first and foremost. They had a paranoid delusion that all Jews have an inborn desire to subvert the nobler Aryan civilisation.

There were non-anti-semitic fascists too like Eoin O’Duffy

Fascist is ultranationalist/chauvinist meanwhile nazi is ethno-nationalist