Norsemen is used to refer to the group of people as a whole who speak one of the North Germanic languages as their native language. ("Norse", in particular, refers to the Old Norse language belonging to the North Germanic branch of Indo-European languages, especially Danish, Icelandic, Swedish and Norwegian in their earlier forms.)
The meaning of Norseman was "people from the North" and was applied primarily to people from southern and central Scandinavia. They established states and settlements in areas which today are part of the Faroe Islands, England, Scotland, Wales, Iceland, Finland, Ireland, Russia, Italy, Canada, Greenland, France, Ukraine, Estonia, Latvia, and Germany.
Norse, Norsemen, and Normans are all applied to the Scandinavian population of the period from the late 8th century to the 11th century. The term "Normans" was later primarily associated with the people of Norse origin in Normandie, France, assimilated into French culture and language. The term Norse-Gaels (Gall Goidel, lit:foreign Gaelic) was used concerning the people of Norse descent in Ireland and Scotland, who assimilated into the Gaelic culture.
Vikings has been a common term for Norsemen in the early medieval period, especially in connection with raids and monastic plundering made by Norsemen in Great Britain and Ireland. Northmen was famously used in the prayer A furore normannorum libera nos domine ("From the fury of the Northmen deliver us, O Lord!"), doubtfully attributed to monks of the English monasteries plundered by Viking raids in the 8th and 9th centuries.