A separatist movement is generally one where a group wants to secede and become their own country. See Alberta in Canada.

An independence struggle is where a people are trying to remove an occupying force, their colonizer.

Very similar, but not quite.

> Why would that matter? Would it be okay if they were the same race? How do you define race?

It matters when the colonizers are racial supremacists who look down on your culture, traditions, and way of life. And as a result of their POV, they confiscate your lands (because they don't accept your unwritten land ownership "titles"), wipe out your men, and replace you with their own people.

> How do you define race?

Head over to reddit where your trolling will be welcomed.