Let's start with definitions:
REO is an acronym for Real Estate Owned (by banks, investors, hedge funds, etc.) For all practical purposes REO, bank owned homes, and foreclosures are terms used interchangeably. Because I'm a lazy typist, REO is my favored term. However, when you see bank owned property, foreclosed home, or other similar terms here, they all refer to property that has been through the foreclosure process and is now available for sale.