Plutocracy is government by the wealthy: An elite or ruling class (plutocrats) whose power derives from their wealth. (Courtesy © Academic Dictionaries and Encyclopedias); Plutocrats are distinct from Philanthropists who are also wealthy but use their wealth for the public good.
Oligarchy is government by a few powerful people;
Aristocracy is government by the self-proclaimed best people who are often the descendants of Plutocrats.
Moreover, “the risk of a drift towards oligarchy [i.e., Plutocracy] is real and gives little reason for optimism about where the United States is headed.” (Piketty, Capital in the 21st Century, Courtesy © Wikipedia)