The Nordic countries comprise Denmark, Finland, Iceland, Norway and Sweden. Scandinavia is basically your geographic definition; it's not quite clear cut, though, but we mostly care about being Nordic. Finland is the odd one out in terms of linguistic roots, but we share most of our culture with the Nordics -- we were basically a province of Sweden for centuries, and gained independence after a brief stint with Russia.
For some odd reason people elsewhere say "Scandinavian" when they mean "Nordic".
I wonder where you get the part "north Finland speaks partly swedish". There is a vocal Swedish-speaking minority in Finland, but they mostly live on the coast of the Baltic Sea. Might be some Swedish/Norwegian speakers up North, but there you also have the Sami people of Finland, Norway and Sweden mixing up things and blurring the political boundaries.