Plutocratic is the adjective for plutocracy and plutocrats. It describes a government, a class, a habit, or a country when rich people hold the power — and, like its family, it is typically used with a frown. A plutocratic elite, plutocratic interests, a plutocratic system: money rules, or is said to. The line you may have seen that treats it as "someone who is rich and powerful" is really the noun plutocrat; this word names the flavour of that power, not the person as a job. It is formal, written English. Though actually, writers sometimes pin it on anything expensive and exclusive ("a plutocratic lifestyle"), stretching it from "rule by the rich" toward "the rich at play". The tighter sense is still about power, not only about taste.