A country is a region of people where a sovereign government governs them.
Example: India, United States, United Kingdom
On the other hand, a nation is a group of people bound together by a common language, identity, ethnicity, history, culture etc.
Example: Scotland is a nation but not a country. It is one of the regions governed by the United Kingdom.
Puerto Rico, a territory of the United States of America, is considered as a nation but not a country.
India is considered both as a country and a nation since it has a sovereign government, and people are bound together by common ethnicity and culture for thousands of years.