When both sides agreed to stop fighting in Korea, they signed an agreement known as an Armistice.
An armistice is a formal agreement of warring parties signed by the parties in order to stop fighting. It does not mark necessarily the end of a war, since it may constitute only a cessation of hostilities while lasting peace may be negotiated.
An Armistice is not considered a peace treaty, it is a modus vivendi.
The 1953 Korean War Armistice Agreement is a very important example of an armistice which has not been followed by a peace treaty.