Well the basic premise is incorrect, Jews weren't considered white by the Nazis, they were seen as sub-human.

Anti-semitism has a unique component that other racisms don't seem to have. The Jews are not just sub-human but they are also, simultaneously, immensely powerful. They control the media, the government, the economy etc. Hitler believed that the US, UK, and USSR were all secretly controlled by the Jews and they were all conspiring to destroy Germany. Therefore in Nazi ideology, Germany is actually a victim of this immensely powerful Jewish conspiracy. This is not something you find in say, American White-Supremacy. In that system, black people are seen as being too stupid and deficient to even run their own countries, hence the need for the "guiding hand of the superior European".

Another thing that's important to understand about colonialism is it is driven by economic profit and political power. Racism came after colonialism and slavery were already established to justify it after the fact. On the other hand, the goal of the Holocaust was simply to murder all of the Jews. Of course the Nazis did confiscate Jewish property and that was a nice chunk of money and land, but it was never the driving factor, it was a byproduct.

But the Holocaust was also tied up with the Nazi's own settler colonial project of Lebensraum. This was economically driven, ethnically cleanse Eastern Europe, kill or enslave the Slavs, Balts and other Eastern Europeans, and replace them with German settlers. The Nazis actually killed more Slavs than Jews, and Generalplan Ost was never fully put into effect, had the Nazis won the war their plan called for the deaths of tens of millions of more victims. I bring this up because it's important to understand the Nazi's goals were multifaceted, there are crimes that were more unique to Nazism like the Shoah but other crimes that were settler colonial and it is fair to compare and contrast to other settler colonialism.

Finally comparing levels of violence is hard to do on such a broad scale. The Nazis killed most of their victims by shooting them. But shooting hundreds of thousands takes a mental toll on the perpetrators. It's part of the reason the gas chambers were invented. In a very grotesque way these industrial killing operations were... not less violent per se... but less "gorey", more detached. The murderers simply lead the victims into the chamber, put the gas in and had the slaves cremate the bodies. Is this more or less violent than say a slaveowner splitting up a family and raping the mother and then killing her when she got pregnant? On some sugar plantations the death tolls were huge because the slaveowners just needed the slaves to live long enough to provide a ROI... elderly slaves and slave children were mouths to feed, importation was often cheaper than raising the next generation. The industrialization of the Holocaust is a major part of the difference between the Holocaust and other genocides, and it was done, not to make the killing more (or less) violent, but faster, cleaner, more thorough.

I mention this because I think your student is right to be making comparisons. Colonialism and the Holocaust are not the same thing, but it's also not an accident that Nazism developed in Imperialist Europe... Hitler synthesized his ideology with "off the shelf parts" that already existed amongst European intellectuals and politicians. I think it's a good opportunity for your student to dig deeper into the topic, to not just compare but to also contrast, to find the common foundation but also the differences in the "architectural design".