What's the common definition term of social ranking by social wealth

I would assume that you are looking for "social class".

what term would be use to an oppressor uses race to determine who is and is not privileged.

racial discriminator would be a good term.

The commonly used term for social ranking based on social wealth is "socioeconomic status." Socioeconomic status combines an individual's economic resources, such as income and wealth, with their social standing and level of education. It is a way of categorizing and understanding the different positions individuals have in society based on their financial resources and social prestige.

To determine someone's socioeconomic status, you generally need to consider several factors. These may include their income level, educational attainment, occupation, and sometimes even their family background or social connections. By analyzing these elements, you can assess where someone stands within the social hierarchy in terms of their wealth and social standing.

It's important to note that socioeconomic status is a complex concept with various approaches and measures. Different societies and researchers may use slightly different definitions and indicators, but the general idea is that socioeconomic status captures an individual's position in society in relation to their economic resources and social factors.