Understand 'Norman' as key in English history, signifying a cultural and political change after 1066. The Norman influence can be seen in many English castles.
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Geographic Origin
'Norman' specifies someone from Normandy, not just any part of France. Joan of Arc fought against the Normans in her battles.
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Not Contemporary
Today, it's rare to refer to someone from Normandy as a 'Norman'. You might see a 'Norman' reenactor at a historical event.