traditional county

Short definition from Wiktionary

Noun

1. 1
   A county without direct administrative functions. e.g. Yorkshire, Perthshire, Dublin or Suffolk County, Massachusetts.
2. 2
   any of the historic divisions of Great Britain no longer used for administrative purposes in favour of ceremonial counties and administrative counties
3. 3
   any of the historical sub-national divisions used for the purposes of geographic demarcation, local government, and sport.