I go along with my eighth grade geography teacher about this.
Strictly speaking "Scandinavia" is only Denmark, Norway, and Sweden. That because Danish, Norwejian, and Swedish, form the Northern Germanic language family of related languages spoken by the related tribes that settled the what are now those three countries in ancient times.
Finnish is a separate language that is not Germanic, and not even Indoeuropean, but is an offshoot of the Uralian language family spoken by aboriginal tribes in western Siberia.
However the Vikings of old settled the Shetland island, the Orkneys, Iceland, and Greenland. Greenland is still owned by Denmark, and Iceland folks speak a Norse language in the same Scandanavian language family as Danish, Norwejian and Swedish. So Iceland and Greenland might thought of as "Greater Scandinavia".
Finland was sometimes ruled by Russia, and sometimes ruled by Sweden (the Swedes were the more oppressive), and only became an independent nation after WWI. But Finland is very Scandinavian in culture, and its coastal regions are largely Swedish speaking. So you can use the term "Finnoscandia" for "Scandinavia plus Finland". Or you could just call them "the Nordic countries".