I haven't seen the movie, so I'm not sure how to compare.

The Korean War was mostly fought within the first year from Jun 1950 until June 1951. From then onward, the two sides began meeting in Kaeseong and then Panmunjeom for truce negotiations. During that time, most of the fighting was over strategic hills along the front line in order to secure a better position once a truce was signed. That's not to say that there were not horrific battles in '52 and '53 - Baekmagoji (White Horse Hill) resulted in upwards of 10,000 killed or wounded on both sides and the artillery fire leveled the mountain into the shape of a horse (hence the name). The Battle of Triangle Hill right afterwards resulted in upwards of 25,000 causalities, and Pork Chop Hill in the summer of '53 went up to three weeks before the Armistice was signed. There were nearly 5,000 casualties from that battle. The Battle of Kumsong River continued right up to the Armistice. The USAF continued bombing campaigns and a B-29 dropped bombs just hours before the armistice went into effect as well.

As I said, I haven't seen the movie, so I don't know how it's depicted, but the war continued up to the day of the armistice, although even the Battle of Kumsong had died down about a week before.