EDIT: Actually, after looking it up, this is interesting: In most languages except English, Switzerland is referred to by the adjective. That is, in Italian it's "Confederazione Svizzera," or just "Svizzera" for short, in French it's "Confédération suisse" or "Suisse"... huh!
"Welcome to the official website of the Swiss Government", quoting from https://www.admin.ch/gov/en/start.html
The country is Switzerland; if you are from Switzerland you are Swiss.
Not the best example perhaps, as strictly speaking the British Government (or more formally Her Majesty's Government) governs the United Kingdom (which is a sovereign state or country), not just the geographical region of Great Britain (which includes the countries England, Scotland, and Wales).