No. Classes aren't castes. You can change class but not castes. In this way it is more like social-racism. I don't think the surnames "Gates" or "Rockefeller"

No. Classes aren't castes. You can change class but not castes. In this way it is more like social-racism. I don't think the surnames "Gates" or "Rockefeller" are reserved or showing to which caste/class they belong. As for group A feeling superior to group B, it's common everywhere and is purely subjective. Unlike a caste system that has some real everyday-life consequences.