indigenous and colonized are more or less synonyms, its not really a proxy of anything. Why specific word is used instead of another to refer to something is a question more suited for linguists. But if I had to make a guess, I'd venture to say that people prefer to use a term to describe themselves that doesn't center around the negatives.
I don’t think that’s true. I don’t think the Welsh or Irish are on anyone’s list of indigenous peoples, for example. Maybe “colonized” has some specific academic meaning that I’m misapplying to the Welsh, Irish, etc.