The Nazi party doesn't exist any more. American wannabees are not Nazis, and most of them look like their applications to join would have been refused.
There are plenty amongst the US far right, and their European counterparts, whose political ideology is based on a racialised form of fascism and who believe in a Jewish conspiracy to control the world and as such Jewish people should be eliminated. At the more extreme end these groups will use the regalia and symbols of the Nazi Party, including idolising or acting as apologists for Hitler. It's not unreasonable to call these groups Nazis, if you want to add neo fair enough but it doesn't seem to me to be worth nitpicking about. They are almost always present at far right events and less extreme far right groups in the US have been happy to march and fight alongside them, as theyoften share some if not all of the same ideals.
The far right are not all the same, but what unites them is first a desire to destroy any gains working class people have made, or ever could make, such as dismantling public services, employment protection, LGBT and women's rights and preventing trade union or organised left wing activity. There's a reason they came for the communists first, and they are still at it - far right movements when they take hold always begin violently attacking the left.
What these groups also share is a belief in natural hierarchies, whether based on race, culture, sex, or sexuality and a desire to return to a society based on those hierarchies often based on idealised and mythical notions of some noble past that has been destroyed by feminists, immigrants and gays. Some will proudly proclaim themselves anti-racist like Tommy Robinson whilst whipping up mobs to march into Muslim areas, some have a religious perspective, some favour white supremacy, mass deportations and racial segregation. Some are media savvy and recognise the value of not showing your true face, or only attacking certain minority groups whilst pretending to defend the others whilst some insist on being open and drape themselves in Nazi regalia. Some will deliberately attempt entryism to stir up racial tensions, when the BNP were at their peek some were openly attempting to court Muslim groups with anti-Semitic, anti-Israel propanganda whilst simultaneously courting Zionist (in the true sense of the word) groups with anti-Muslim propaganda. And some, particularly in the UK, are just drunk racists who like a fight and are attracted to the movement for that reason alone.
Most importantly what these groups share, and the way they can be recognised as far right as opposed to the more extreme conservatives and Tories, is a commitment to using violence to pursue their ideals - see the storming of the Capitol for details or the countless and sometimes murderous attacks on people of colour, minority owned businesses and left wingers carried out by far right forces across the globe. So whilst within them they may be different factions and even disagreement it is not unreasonable when they gather in armed mobs on the streets to treat them as a monolithic and violent block, because in that moment that is how they behave. I don't really care whether people describe those mobs as Nazis, Fascists, far right or alt-right, it strikes me the problem is what to do about them not what to call them. Because they are dangerous, and if they are able to take the streets unopposed it will not end there as history sadly shows.