Take a person who believes that "there needs to be a country for white people and white people are innately better able to form productive societies". This person would clearly be a white nationalist and a white supremacist, right?

But they may also have no hate towards other ethnicities or desire their deaths. If pressed, they might even say that their vision of a "pure" society isn't worth the deaths of minorities that would come about if they tried to implement it.

I think too often we confuse the stereotypical example with the definition. The stereotypical white supremacist hates minorities, but the definition itself doesn't require it (I know of no surveys that would tell us what proportion of white supremacists match the stereotype).