Nazism != fascism. Nazism is a type of fascism, but not all fascism is Nazism, for example while Franco’s regime in Spain was fascist, it did not adhere to Nazi ideology. From Wikipedia:

Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. It incorporates fervent antisemitism, anti-communism, scientific racism, and the use of eugenics into its creed.

A Nazi today is someone who strives for an anti-semitic, racist, authoritarian, and hyper nationalistic form of government. This is different from generic facism, which while there are still ‘in groups’ and ‘out groups’, they need not necessarily be anti-semitic or anti-communist. This is why it’s absolutely ridiculous for Putin to call the Ukraine government a Nazi regime, because even ignoring the fact that the country is a democracy the president is himself Jewish.