Isn't it the case that social class is not just about how much money you have, it's about where you went to school, your social etiquette, way of speaking, mannerisms, the clothing you wear, etc?
Isn't social class specifically evolved to not simply be traversed by attaining more money, and that's the whole distinction between "new money" and "old money" and how they say "money can't buy class"?
That being said, I think perhaps the caste system is sort of neither about race nor class but some unique blend of those things and more. It seems to have its own characteristics and I'm not sure we can dumb it down.
