I feel like this needs to be explicitly written out, and probably someone already has, but I mean that I need to do it for myself to help nail some shit down in my head so bear with me.
I'm going to say up front that this is not a "stop calling everyone nazis" post. The reason why will become clear soon.
Average White Person
This is the kind of person who would be horrified to be called a white supremacist and deny it profusely. Yet they benefit from cultural white supremacy and do nothing to change that. They may think that they do something to change it, but their actions are ineffectual at best, and more often actually reinforce the system of white supremacy. They may believe in "color blind" ideology, hold that many racial stereotypes are true even if you shouldn't say it, and have done little if anything to combat subconscious racial biases. This group includes many liberals. There are a lot of them.
In the U.S., these are the people who always vote Republican. They hold conscious negative feelings about people of color and may or may not admit to that, or do so only in certain company. With their votes and dollars, they actively promote systems of white supremacy, even if they do so for alternate reasons (or think they're doing so for alternate reasons) such as for greater wealth, better security for (typically upper class) white people, or some ideology about the "free market." This can include poor whites hoping to someday become rich. If pressed a bit, their racism tends to come out real fast. They often hold nationalistic beliefs even if they do not name them as such or realize that's what they are. They may mislabel their nationalism as patriotism.
A nationalist is outwardly racist but will excuse this racism behind all kinds of twisty "logic" about white culture, national security, pride, and sometimes outdated pseudo-science around biology (*cough* eugenics). They often don't identify as a "white nationalist," and technically you don't have to be white to be a nationalist. But we're talking about white people here and if you're white and a nationalist you're a white nationalist. It's never actually about the nation. The U.S. is a very diverse nation but it's always about race.
Nationalists can often make their views sound semi-reasonable if you just let them talk, but there's no way to force the many millions of people of color out of the country without violence, and plus the people who were here first were NOT WHITE so any argument they make falls apart on those grounds, and then they're just white supremacists who are concerned about their image. They may become violent if confronted or go out looking for fights.
Self-Identifying White Supremacist
These are the less pleasant nationalists who are outwardly, blatantly racist and don't care enough about their image to try and dress it up. They think white people are superior and they don't often feel the need to justify that, or will only use a poor knowledge of history and pseudo-science (claiming that white people invented everything good and are somehow biologically better).
They are often verbally and physically violent to both people of color and any white people who defend them. They may only hide this from the public in order to stay employed, but use anonymous online personas to harass, threaten, and doxx people. They're often also very misogynistic, homophobic, transphobic, ableist, etc. The worst of them are the ones who make up white supremacist communes, trying to live outside of a society that isn't as racist as they want it to be.
This is a weird but important category that may have only emerged very recently. These are the members of the so-called "Republic of Kekistan." They are often young white men (though they can be anybody) who claim to think it's ridiculous that "people" or "liberals" or whoever is "calling everyone a nazi." So they act just like nazis because they think it's funny. Don't think too hard on that one, it'll just give you a headache.
These "Kekistan" people specifically come from horrific underground forums like 4chan and the somehow even worse 8chan. The term "kek" originated from World of Warcraft. I don't have to explain this part but I will. In the game, there are two factions. You must choose one faction, and if you come across another player in the game who is in the opposite faction, they appear to speak in another language. In fact, it's just a simple letter replacement algorithm. Eventually, someone figured out that when a player in the opposite faction appears to say "kek," they're actually saying "lol." For some reason, it then became common for people on these forums to say "kek" instead of "lol."
Then one of these individuals notices that Kek is an ancient Egyptian god of darkness. Being the massive edgelords they are, they decided that they should jokingly or ironically or something "worship" Kek, and then came the notion of the "Republic of Kekistan," because of course. Also, being trolls who think that upsetting people is the funniest thing ever, they took the Nazi flag, turned it green after that fucking frog thing, and replaced the swastika with an emblem made out of the letter K.
All of this is based around an insular, tribal, and very bizarre kind of "humor" that I don't understand, besides the basic idea that causing people pain is funny. They also cling to the small amount of power they can find in numbers, organizing attacks on selected targets via constant harassment, threats, hacking their pages, etc. Basically anybody upset enough by their antics to actually push back gets viciously attacked by them, because their being upset or feeling threatened is definitely not funny.
As you can see, this is the most difficult group to get a handle on. I wasn't even sure where to place them on the list. The line between them and actual nazis is so blurred, and anything and everything they do they're willing to dismiss as a "joke," no matter how horrible. Or, in reference to their attacks, they might say that they were defending themselves, which brings into question how serious they are about this bizarre little tribe they've developed. How invested in a supposed joke do you have to be to so viciously defend you pretend society?
Yet when pressured, they will deny up and down that they are real, true, actual nazis.
These are the rarest of white supremacists, but they are becoming more common.
It's noteworthy that back in the days before the rise of Germany's National Socialist Party, the word "nazi" was a common insult that meant something like "backwards peasant" - basically the old-timey German version of a redneck. When the National Socialist party emerged in Bavaria, a place where the insult was common, opponents started calling them nazis in short for "Nationalsozialistische Deutsche Arbeiterpartei," the German name for the party, but mainly as a derogatory term. Hitler himself hated being called a nazi.
I bring this up to counter the absurd idea that the only people who are nazis are the ones who call themselves nazis (if Hitler wasn't a nazi then um......) but also to point out just how extreme you have to be to self-identify as a nazi. If backed into a corner, these individuals may claim to only call themselves such to upset or anger people, trying to revert to the Pretend Nazi category, but their actions say different. These are the members of the Daily Stormer and neo-nazi gang members dedicated to violence against anyone who is not a nazi and actively promoting and recruiting. Remember, if it walks like a nazi and quacks like a nazi...
The point is that on August 12, 2017, the biggest white supremacist rally in 10 years happened in Charlottesville, Virginia. One person is dead and many more injured after someone rammed their car into a crowd of anti-racist counter protesters. This after the previous night where these racist pieces of shit marched upon a church in which black religious community leaders were having a meeting, including Dr. Cornel West. Antifa was able to slow the torch-carrying mob enough for the church to evacuate safely, but the white supremacists attacked the counter-protest crowd with weapons, including pepper spray and lighter fluid (holy fuck).
These white supremacists, the ones marching on the church and attacking the University of Virginia, were nazis, pretend nazis, self-identifying white supremacists, and nationalists. Conservatives have been silent, with Trump only offering a vague tweet about "both sides."
The average white person may be looking at this with horror, unaware that nazis and KKK members have been active in Charlottesville for, well, since they ever existed. Note that this is the biggest white supremacist rally in 10 years. 10 years isn't that many years! That was about the time when one Senator Barack Obama announced his campaign for presidency.
Average white people may condemn the blatant white supremacists, they may condemn the violence, but don't do anything real to stop it and will go about their lives benefiting from white supremacy.
There are differences between these groups, but they become more blurred as you get closer and closer to straight-up, eugenics-supporting, holocaust-praising nazi. And they are all complicit, and they are all working toward the same goal, whether they realize it or not. There comes a point where the distinctions don't matter anymore. When racists are marching upon black churches with torches, shouting nazi slogans and "Heil Trump," when people are being attacked and murdered for standing up to them. What difference is it if you're a nationalist, or just doing it for the lols, or are just trying to "protect" your race, or are excusing these actions because it's just a few bad apples (it's not)?
I'm not about to let myself off either. No matter how much anti-racist action I participate in, I still benefit from white supremacy every moment of every day of my life. I'm just glad I have the sense to be sickened by it.
In conclusion, if someone is acting like a nazi in any way, call them a fucking nazi. It that offends them or makes them laugh, do it again. Because they are all participating in actions that help actual, self-identifying nazis in their goals, and that needs to be called out for what it is. Don't like being called a nazi, or think it's ridiculous that you're being called one? Don't act like a fucking nazi. Like always, it is an insult, and should be the worst insult. So if someone calls you that, you know you've royally fucked up. And if you think it's somehow okay to do a thing that got you called a nazi, you might as well be a nazi.
Tomorrow I'm going to a counter-protest against yet another white supremacist rally in Seattle. I'll be careful, but wish me luck.