A sheriff is a government official, with varying duties, existing in some countries with historical ties to England where the office originated. There is an analogous, although independently developed, office in Iceland that is commonly translated to English as sherif.
A prisoner transport van used by the Alberta Sheriffs Branch
A British Columbia Sheriff Service Ford Crown Victoria Police Interceptor
Shire is a traditional term for an administrative division of land in Great Britain and some other English-speaking countries such as Australia and the United States. It is generally synonymous with county. It was first used in Wessex from the beginning of Anglo-Saxon settlement, and spread to most of the rest of England in the tenth century. In some rural parts of Australia, a shire is a local government area; however, in Australia, it is not synonymous with a "county", which is a lands administrative division.
Image: Anglo Saxon Chronicle scire (British Library Cotton MS Tiberius A VI, folio 11v)
Image: Anglo Saxon Chronicle scira (British Library Cotton MS Tiberius A VI, folio 9v)