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: 
How is everyone is this thread so wrong about Joseon and Goryeo. 

The name Joseon/Choseon comes from the historical period 2333 BCE-108 BCE. The name "Guryeo/Korea" comes from 37 BCE–668 CE.

Thus the name Choseon predates the name/character "Han" referring to the "Samhan/Three Kingdoms" period, and "Korea" comes immediately afterwards. 

They retroactively add a "Go-", the Chinese word for ancient/older/etc., to the front of both Choseon and Goryeo names to distinguish them from the newer dynasties/periods named after the original ones. 

(Think about how empires based in Turkey and Germany both called themselves Rome or Roman at some point. Just because they were more recent doesn't mean they were the original "Rome" obviously.)
On the rare occasions on which the ROK and DPRK have cooperated in international sporting events (1991 table tennis world championships, summer olympic opening ceremonies 2000 and 2004 and winter olympics women's ice hockey 2018), they have used the name 'Korea'.

In general, though, Koreans use the name 'Korea' *when they speak in English*. At least South Koreans do - I haven't met any North Koreans.