If today's white supremacists found power, they'd look exactly like Nazis. The enemy might be different, but the mindset of fighting that enemy would be exactly the same, and the white supremacist suddenly finding power would find no other example to take heed of than the Nazis, so we can pretty much almost assume that that's what would happen.
Sure, but it's important to realize that this is true about any supremacist ideology. There's nothing exclusive about either Nazism or white supremacism. ISIL's Islamofascism is the same old crap for example, and it too has a line of historical descent from, e.g. early-20th-c. anti-Semitism. The Grand Mufti of Jerusalem was a raging anti-Semite who met Adolf Hitler and ardently supported his most heinous atrocities.
Not so! There is significant, though not watertight evidence that Hitler intended the Holocaust to be followed by mass extermination and enslavement of Slavic peoples (so-called Generalplan Ost), whom Nazi Germans regarded as an "inferior" race according to their racial ideology, and surely not "Aryan" - despite, y'know, Slavic languages sharing a common ancestry with both Germanic languages and Indo-Iranic ones! Nazi German attitudes to the "supremacy" of race, culture and the like were a lot weirder than people are usually ready to admit these days; while they may have been rooted in some sorts of shared vocabulary from the early 20th-century, to a far greater extent they were just "Nazi Germany and the friends of Nazi Germany good, everyone else bad!" Of course, this is the story of supremacist ideologies everywhere; but the point is that we should not grow complacent and reassure ourselves that there's anything especially peculiar about white-supremacist nationalism; it's just one of many, many ideologies with broad similarities in their appeal to hateful sentiment.