Taxonomy.

A cat is [animal] A dog is an [animal]

The nazi’s did such a good job of distinguishing themselves they created their own (colloquial) taxonomic branch.

So [nazi] could be considered a parent grouping of the National Socialist German Workers’ Party and also potentially a parent grouping for the republicans.

I think they key here is separating the nazi party from the [nazi] category

As you pointed out all [nazi]'s are [fascist]'s but not all [fascist]'s are [nazi]‘s

National Socialist German Workers’ Party were [nazi]'s The American Republican Party are subjectively showing enough similarities (both in type and progression) that they get the provisional label of [nazi] as it’s the closest existing definition.

Might turn out that they don’t quite fall in the same branch, might turn out they do. Until then [nazi] is an easy shortcut for describing the types of behaviour displayed.

Come back in a few years and you’ll probably get your definitive answer.

You don’t have to agree with any of that of course, but it does demonstrate how someone might have an opposing opinion to your own.