The geographical terms "Near East" and "Far East" referring to areas of the globe in or contiguous to the former British Empire and the neighboring colonies of the Dutch, Portuguese, Spanish and Germans, fit together as a pair based on the opposites of far and near, suggesting that they were innovated together. They appear together in the journals of the mid-19th century. Both terms were used before then with local British and American meanings: the near or far east of a field, village or shire.
The term Near East and Far East were used in British and American meanings when referring to what? 
the near or far east of a field, village or shire.