Neither North Korea, nor South Korea recognises the government of the "other half".
So from the point of view of the South, North Korea is composed of five "provinces" (dō), with two more provinces having part of their territory North of the AmisticeArmistice line. South Korea appoints governors for these provinces, but their role is symbolic. See (the committee for the five Northern Provinces](https://en.wikipedia.org/wiki/Committee_for_the_Five_Northern_Korean_Provincesthe committee for the five Northern Provinces)
The situation in the North is similar. Pyong-Yang does not recognise the Governmentgovernment in Seoul.
The major difference with China is that the rest of the world recognises two sovereign states, one in the North and one in the South. Both have seats in the UN and some countries (eg Sweden) even have diplomatic relations with both.