As mentioned in the late 9th century Old English Orosius, Norway (which at the time consisted of various petty kingdoms in parts of what is now Norway and Sweden) was then called Normanna land or Northmanna land, and its inhabitants Northmen (Old English: Norðmen) (Barrington 1773:13). This is equivalent to the current Norwegian demonym for Norwegian (“nordmann”). Since the ‘d’ in nordmann is silent, it has the same pronunciation as Norman. Both demonyms share the same etymology, as both are derived from the Old Norse Northmathr, meaning Northman or Norseman. It is therefore likely that both demonyms initially also shared the same meaning.
Literature
Barrington, Daines (Tr.). The Anglo-Saxon version, from the Historian Orosius by Alfred the Great. London: Oxford University School of English, 1773.