One of the Baltimore Orioles' biggest rivalries actually has very little to do with head-to-head competition. The Nationals don't play in the AL East or even in the American League, but these two teams have a regional battle for fans that goes back to when the Nationals returned, starting with the 2005 season. The two teams were even embroiled in a lengthy legal battle over local TV rights fees that only recently seems to be mostly settled (for now).
While there doesn't seem to be any hard feelings over the lawsuits, there is no denying that Baltimore and Washington are fighting over the same group of baseball fans, and that is going to create a rivalry.