An armistice is a formal agreement to stop fighting. It could be for a few hours, days, weeks, or months. It doesn't mean that the war is over it simply means that there will be no fighting for a set amount of time. There had been a recent armistice in Syria. There was supposed to be a pause in the fighting, but the war was still going on and had not formally ended.
A peace treaty is an agreement that formally ends a war or fighting between the two sides. Treaties appear after every war: American Revolution-Treaty of Paris 1783; War of 1812- Treaty of Ghent; WW1- Treaty of Versailles. A Peace treaty is a more permanent solution whereas an armistice is often only temporary.