Question: [The Wikipedia article on Korea](https://en.wikipedia.org/wiki/Korea) states that South Koreans call Korea 한국, while north Koreans call it 조선. Do 'Korea', '한국', and '조선' all refer to the same thing? If so, how did the three different names come about?

Answer: 
Usually, 'Korea' and '한국' refer to South Korea(Republic of Korea, 대한민국), and '조선' indicates North Korea(Democratic People's Republic of Korea, 조선민주주의인민공화국).
고조선 ->... ->고려 (Korea) -> 조선 (Joseon) -> 북한,
남한(=한국=대한민국)

Korea is from 고려 so that for 남한, republic of Korea, Korea, and
south Korea are possible.

And for 북한, Joseon and north Korea are possible.