The caste system in India is very complex, but at its most basic level consists of the categorization of all Indians into four groups based on their traditional occupations: Brahmins, Kshatriyas, Vaishyas and Shudras. There is an implicit fifth class of Dalits and Adivasis, the "untouchables," and then there are tribal people who are outside these four castes.
The caste system is still an important system of social stratification in India. It is broadly correlated with wealth and power. However, while it is still relatively uncommon to find a Shudra or Dalit in a high position, it is very common to encounter a Brahmin who is comparatively poor.
The American class system, by contrast, is much more closely correlated with wealth. While it has become more rigid in recent decades, it is still more flexible than the caste system, which is based entirely on birth. A Brahmin who is poor is still a Brahmin and a Dalit who becomes rich is still a Dalit, but in America one changes class as one's income rises or falls. A multi-millionaire might have working class origins, but is not himself regarded as working class. Even those members of the upper classes who do see the self-made millionaire as a parvenu would probably accept his children, who have been educated at expensive preparatory schools alongside their own, as being part of the same class.
The New England upper classes are sometimes described as "Boston Brahmins," suggesting a link between the American class system and the Hindu caste system. However, there is a significant difference in that everyone in India is aware of the caste system and its distinctions even if they regard these distinctions as unimportant. In America, it is often said that the closest thing to royalty is the Kennedy family. Even the Kennedys are far from being Boston Brahmins, since their fortune is of a comparatively recent date. Within the closed circle of the Boston Brahmins themselves an Emerson or a Winthrop might be far more impressive than a Kennedy, but the public at large would disagree.