Taiwan is self-governing, has its own armed forces, passports, and fully controls its own borders. That makes it a nation, no matter what you want to call it.
A nation requires none of those to be a nation, look at indigenous nations in the US and Canada.
A country needs to be self-governing, autonomous, and recognised by the majority of UN members. Taiwan isn't recognised by any country of note, including the US, so they fail the country test.
Do tell what you think is the criteria for a country being one. Is Transnistria one? South Ossetia? Taiwan? A native American tribe? The US? An American state? It's a trick question!
A native American tribe is a nation, by definition [1]. Heck, the Canadians call theirs "First Nations".
A country requires sovereignty over some land, people, and international recognition. Without the last part, Sealand was a country. Funnily enough, depending on how strict you're with the criteria, some native American tribes are countries, and the US isn't always one due to reservations and states sovereignties.
1 - `a large body of people united by common descent, history, culture, or language, inhabiting a particular country or territory` Oxford English dictionary
A country needs to be self-governing, autonomous, and recognised by the majority of UN members. Taiwan isn't recognised by any country of note, including the US, so they fail the country test.