To what extent was the Korean war a limited war, as well as truly civil war in the context of the raging Cold War?
Geographically, the war was indeed limited. Although within the year MacArthur threatened to extend the war into China and unleash Chiang Kai-Chek, it never went beyond Korea's borders. When the US army moved towards the Yalu river into China's territory, 250, 000 Chinese suddenly streamed over the border surprising the US forces. This culminated in the battle of Chosen which saw US forces pushed all the way back behind the 38th. So committed was the Truman administration to keep this a limited war that he actually fired his commanding officer by April 1951 for 'insubordination' after he went public with a desire to 'nuke' Beijing and start the process of rollback first formulated by NSC-68 (April. 1950). This allowed the West to continue its policy of containment which meant that the conflict had to remain localised, whether along the Iron Curtain in Europe or the 38th parallel.
Nevertheless, it was an expansive war in terms of participants. For example, by the end of 1950, there were more Chinese soldiers than DPRK troops. Even if Kim il Song wanted an end to the war, Mao held all the cards. The same held true in the south where the US was head of a 17-country force under UN auspices. This also questions the idea of a truly 'civil war'. Legally it would fall under this category, being initiated by the North against the South for political reasons (communist vs. 'democratic', to unify a country only arbitrarily divided into 2, which UNTCOK had claimed in '47 to be temporary). However, it was very much a global war of ideology whose consequences would be felt along the newly-divided Germany.
For such reasons, the Korean war stands as an anomoly; one that remains to this day difficult and demanding to define.