In US usage, counties are almost always designated as such, with the word "County" capitalized and following the name — e.g., "Lewis County", rarely "Lewis", and never "County Lewis".
In British and Irish usage, counties are referenced without designation — e.g. "Kent" and never "Kent County". Exceptions are; Durham, which is often "County Durham" (but never "Durham County"); and the counties of Ireland. An organisation such as Kent County Council is the "County Council" of "Kent" and not the "Council" of "Kent County".
In Canadian usage, counties are typically designated as such, with the word "County" capitalized and usually preceding the name — e.g., "the County of Two Hills". Occasionally, "County" follows the name, as in "Sturgeon County".
Characteristic of a ‘county family’; representative of the gentry or aristocracy of a county.
1886, Andrew Lang, The Mark of Cain:
Now, in the district around Chipping Carby, the County Families are very County indeed, few more so.
1979, John Le Carré, Smiley's People, Folio Society 2010, p. 274:
She was a tall girl and county, with Hilary's walk: she seemed to topple even when she sat.
2007, Heather Julien, Gender and Literacy in Britain, 1847--1987, →ISBN:
The other two, like many of her characters, have fallen on harder times: Joan's family has recently lost her father, a small flour-mill owner -- described by a supporter as more "county" than the upstart newcomers who covet their property ...
2015, Kate Macdonald, Novelists Against Social Change: Conservative Popular Fiction, 1920-1960, →ISBN:
Susan Dean realises that her secretary, Eleanor Grantly, is much more county than she ever will be, because Eleanor knows all the Barsetshire family connections and is connected herself.