You are right regarding Corean being the God of the Smith and Paladins in Scarred Lands. Regarding Corea not equalling Korea however, I'm sorry, but that's where you are misinformed Corinth (if you watch the football games Corea is involved in carefully, the Corean support crowd is waving "Corea" bands all over). A brief historical lesson up ahead...
Long ago, about 5000 years, there was a nation formed by former hose lords, called the People of Han, in a peninsula. They were a nomadic group that broke away from the Mongols and Turks (the Coreans share a common ancestors with the aforementioned cultures, the Altaii is what I believe they were called). Much later, advance the time to the Middle Ages, the western explorers found a unified nation called Corea (there were many kingdoms that rose and fell all with different names) in the same peninsula and thus dubbed the people there Coreans. Advance the time to the Japanese occupation of early 1900's, after the fall of Corea and Chosun dynasty, and you have Nipon (namely Japan) changing the nation's name of Corea into Korea, just simply because C came before J while K did not. Reasons were political and emotional back then; the Coreans would prefer to be named with the C instead of the K. End history lesson.