The term "business oligarch" is almost a synonym of the term "business magnate", borrowed by the English-speaking and western media from post-Soviet parlance to label those businessmen who quickly acquired huge wealth in post-Soviet states (mostly Russia and Ukraine) during the privatization in Russia and in other post-Soviet states in the 1990s. For the history of business oligarchs in post-Soviet Union states see:
A typical example of a post-Soviet oligarch entity is the Privat Group - a large Ukraine-based transnational business conglomerate comprising dozens of industrial companies in several markets, controlled by only three stakeholders, and not through the stock exchange.
More generally, an oligarch is a "member of an oligarchy; a person who is part of a small group holding power in a state". Aristotle gave the concept of oligarchy some negative connotations, but the term does not necessarily imply wealth. Compare "plutocrat".