"Norse" is the name we give to the Germanic tribes who emigrated and settled in Scandinavia around the year 1000 BC. In the 8th century AD, the Norse started building fine and very versatile ships that allowed them to travel long distances. This was the beginning of the Viking age.

The Norse society was composed by farmers, slaves and chieftains or aristocrats. Helped by the speed of their ships, some of the farmers and chieftains would become pirates during the summer and would go to raid and pillage foreign villages. These were the Vikings.

"Viking" was a verb used to describe a temporary lifestyle. Most Norsemen would stay in their villages for all their lifes, but some young and adventurous farmers would go "viking" or raiding for some months or for some years to earn their living on piracy.

Therefore, all Vikings were Norse, but not all Norsemen were Vikings.