Sometimes The Same, Sometimes Not
Although nowadays they are often used interchangeably, the meaning of country and nation can also be very different in real life, as illustrated using, for example, the United States and Japan.
Japan is one country, and since the population of Japan is over 99.5% ethnic-Japanese people, it could also be called one nation.
The United States of America is one country, and it can of course also be correctly called one nation in a modern political sense, but as the "melting pot" analogy illustrates, the population of the U.S. is made up of people of many ethnic nationalities, or nations. Natural-born Americans can often be heard referring to themselves as "Swedish-Americans," or "African-Americans," or "Chinese-Americans" etc. - even though they, and sometimes their parents, and even their grandparents and great-grandparents may all have been born in the United States.
Clearly, country and nation can take on a much wider and deeper perspective - just as it did recently when natural-born Americans of Jewish descent and natural-born Americans of Palestinian descent were shown on TV-news actually fighting each other in the streets of Los Angeles in response to the latest crisis on the other side of the world in Israel. Americans were fighting Americans as an ancient struggle between nations that began thousands of years before the United States came into existence.
The Biblical Perspective
The difference that sometimes exists between country and nation is very important when studying Bible History, when people were scattered over the earth, and Prophecy, which deals with, among many other things, a future time when people, including the so-called "Lost Ten Tribes of Israel" (who are not Jews - see Hebrew and Jews At War With Israel) will be gathered together again.
"As a shepherd seeks out his flock when some of his sheep have been scattered abroad, so will I seek out My sheep; and I will rescue them from all places where they have been scattered on a day of clouds and thick darkness. And I will bring them out from the peoples, and gather them from the countries, and will bring them into their own land; and I will feed them on the mountains of Israel, by the fountains, and in all the inhabited places of the country. I will feed them with good pasture, and upon the mountain heights of Israel shall be their pasture; there they shall lie down in good grazing land, and on fat pasture they shall feed on the mountains of Israel. I myself will be the shepherd of My sheep, and I will make them lie down, says the Lord God. I will seek the lost, and I will bring back the strayed, and I will bind up the crippled, and I will strengthen the weak, and the fat and the strong I will watch over; I will feed them in justice." (Ezekiel 34:12-16 RSV)
"Therefore say, 'Thus says the Lord God: Though I removed them far off among the nations, and though I scattered them among the countries, yet I have been a sanctuary to them for a while in the countries where they have gone.' Therefore say, 'Thus says the Lord God: I will gather you from the peoples, and assemble you out of the countries where you have been scattered, and I will give you the land of Israel.'" (Ezekiel 11:16-17 RSV)
"I will bring you out from the peoples and gather you out of the countries where you are scattered, with a mighty hand and an outstretched arm, and with wrath poured out; and I will bring you into the wilderness of the peoples, and there I will enter into judgment with you face to face. As I entered into judgment with your fathers in the wilderness of the land of Egypt, so I will enter into judgment with you, says the Lord God." (Ezekiel 20:34-36 RSV)
"And the people of Judah and the people of Israel shall be gathered together, and they shall appoint for themselves one head; and they shall go up from the land, for great shall be the day of Jezreel." (Hosea 1:11 RSV)
Fact Finder: How was the world populated after the Flood?
See Sons Of Noah