Politically, "Scandinavia" and the "Scandinavian countries" have a different meaning.
The Political Scandinavian Countries:
These 3 countries have similar languages, culture, and history, and are always considered politically a part of Scandinavia.
Different definitions also include Finland, which is on the peninsula and has been closely connected to the rest of Scandinavia (particularly Sweden) throughout history. However, Finland is not as closely related to the others; and the Finnish language is very different to the other Scandinavian languages (though most Finns do speak Swedish at some level.)
Other definitions of Scandinavia even include the Danish constituent countries of Greenland and the Faroe Islands, as well as Iceland. These are all far from the Scandinavian peninsula itself, but have strong links with Scandinavia.
Scandinavian politics are dominated by Liberal and Social Democratic parties, and because of this, they are the happiest (Denmark), healthiest (Sweden), most peaceful (Sweden), freest (Finland) and richest-per-capita (Norway) countries in the world. All of the Scandinavian countries, Denmark, Norway, Sweden and also Finland, Iceland, and the Danish constituents - have universal health care.