The word “Norse” doesn't just refer to Norsemen of Scandinavia, Norse also refers to a language which is called the Norse language. A North German language. Which was spoken from AD 800 to AD1300, was referred to as old Norse.
From this Old Norse, east Norse that was modern Swedish and Danish, and also some other west Norse languages were developed. “Norse” in terms of history refers to the Norse mythology, their art, and also the paganism. On the other hand, Vikings, in recent times, are the mythical German people who were noble savages.
But then Vikings were actually Norse explorers; some were pirates, some were warriors who travel by boats to a distant part of the world to trade and also to conquer parts of Europe, Asia, etc for the purpose of expanding and settling down. This expansion actually took place in the Viking Age when Vikings were very powerful and their wars were led by Jarl.