The point of all that was never to establish some logical schema for differentiation...it was simply to discriminate against people. You just say they're Dominican, and their inferiority is thereby firmly established and explained.
Crazy, right? To understand, you've first gotta grasp that discrimination isn't unique to Americans. Everybody does it, and the USA isn't even in the top ten places where arbitrary prejudice makes people's lives miserable.
Next, you've got to grasp that 500 years ago Europeans invaded the western hemisphere and saw themselves as the only real agents of their God's will in all the Americas. That left people in the USA, (where most voluntary immigrants were white-skinned, Protestant, English-speaking, and who came directly from western and northern Europe) thinking that the rightful, God-ordained owners and rulers of the country WITHOUT EXCEPTION combined all four of those characteristics.
So their coded language for describing all other, inferior sorts of people revolved completely around any EXCEPTIONS that any other person might have to that four-way rule. Why say "he's pale skinned, but he doesn't speak English and he's Catholic, and his ancestors didn't land here from western Europe", when you can just skip all that and say "he's Dominican" or "he's a Papist" or "he's a sp ic" (meaning he "speaks" Spanish"). There are dozens of ways to impeach someone's membership in the ruling class, and any one of them is just as good as any other.
You should understand that, over the past three generations, more and more members of this USA "ruling class" who can claim to meet the four-way rule have come to reject the idea that they are inherently superior to anyone else. At this point, those who continue to accept that whole-heartedly are a very small minority. However, a LARGE minority still struggles with various prejudices that they've inherited from previous generations.