No, the term "Nazi Party"refers to the National Socialist German Workers' Party. The term "Nazi" refers to an adherent to the ideology of Hitler Fascism. The NSDAP didn't typically refer to themselves with that term.

There's also a square/rectangle situation in play: all Nazis are fascists but not all fascists are Nazis. In this case, though, he's more on the square side of the comparison. The biggest departures from the ideology are the inclusion of religion and the lack of Lebensraum (at least at home; there's an ironic argument to be made about how his belief that Bibi is moving too slowly in Gaza indicates that he has an eye towards creating living-space for certain groups at the expense of others).

The distinction between a "real" Nazi and a Hitler fanboy is too fine to matter.

He wants to be Hitler, so that's close enough for me.

If he walks like a nazi, talks like a nazi and acts like a nazi. He's a fucking nazi.

The main difference, as I understand, is that national socialism is inherently racist and puts the (Aryan) race on top of the ideology, everything else must submit to the benefit of the (Aryan) race, whereas fascism puts the benefit of the state on top.

https://historyplex.com/difference-between-fascism-nazism

Trump, as far as I can judge from beyond the pond, is still claiming to put the state, or the United States of America, first, like a fascist would do. His hate speech against immigrants still serves the narrative of them being bad for the US, not of them being disadvantageous towards the benefit of the Aryan race.