England does not really have counties – it has shires. The fundamental subunit of the English state was the brainchild of Alfred the Great, who reorganized his kingdom of Wessex to meet the threat of Danish invasion from the north. He defeated the Danes at Eddington in 878, and then proceeded to reconquer England from them, imposing his new system as he went. Eventually Wessex expanded to include all England, and reflecting this fact, the names of most English “counties” end in -shire, for instance Leicestershire, Worcestershire, Lincolnshire, or Hertfordshire. If a shire enjoyed an independent existence prior to Alfred’s conquests it might retain its old name, e.g. Kent, Essex, or Cornwall, but don’t be fooled, these too have been reduced to the status of shires. (This is why there is no County Wessex – England itself is Wessex.)
I assume that the Normans started calling them counties after 1066, given that that was the name they were familiar with on the continent, a name that has stuck. But they are not counties in the French sense of the term, because they are not the private fiefdoms of nobles called “counts.” To this day there are no counts in England – the equivalent noble rank being an “earl” – an Anglo-Saxon term related to the Scandinavian “jarl” (chieftain). But the counties are not earldoms either – such English nobles may have been landowners, but their holdings were scattered here and there – they did not possess their fiefs in return for exercising governmental functions on the local level, as did the vassals of the French king. Instead, the (usually non-noble) shire-reeve, a royal appointee, was in charge of tax collection and law enforcement in his particular shire. William the Conqueror liked this setup and continued it, and the sheriff remained an important figure in medieval England.
So “county” might have replaced “shire,” but “count” did not replace “earl” (although the wife of an earl is a “countess”).
And if the word “county” is not really suitable to England, how much less suitable is it to America, where titles of nobility are forbidden by the constitution. But I don’t know what American state subunits should be called. Not duchies or satrapies! “Departments” would be nicely republican. Louisiana calls its subunits “parishes” but given America’s separation of church and state I’ve never felt that “parish” is appropriate either.