No, the Democratic People's Republic of Korea (”North Korea”) came about when the peninsula was divided in two after the end of World War II and the withdrawal of occupying Imperial Japanese troops. Kim Il Sung, a Soviet operative, was installed as the leader in the North.
OK, I see it was complicated, but I was right in my impression that it was ended only by an armistice, and that
in October 1950, mass Chinese forces crossed the Yalu and entered the war
... so we are still at war with China, right? They seem to know it, even if we have forgotten.