Yes they twist words and ignorant people listen. The best example is the changing of what used to be called illegal aliens, then became illegal immigrants, to immigrants. Deliberately done so people will equate people here illegals with legal immigrants. No comparison. It was done to paint those against open borders and illegal immigration as racists. The left had a lot of success shaping that issue over the years.
You are correct about why they seem to confuse Nationalist with Supremacist.
This has been done with many issues by the left, and helps them shape the issue their way.
https://www.academia.org/the-origins-of-political-correctness/