Today we distinguish the law as it was in Talmudic times when we were not permitted to extinguish a fire that broke out on Shabbos from today when we can, and why it changed in the medieval ages. First we cover Ch. 16 Mishna 4, rescuing large amounts of food if contained in one vessel and large amounts of clothes with the help of neighbors. Then finally in Mishna 5, we get to the subject of extinguishing the fire itself. In Talmudic times, only indirect causing the fire to go out was possible, and very limited, especially per Rabbi Yosei. That changed in the medieval times when even a small fire could become life threatening because it led to looting, pillaging, fighting and pogroms by Jew-hating neighbors. Today, we put out any fire that breaks out on Shabbos unless it is so insignificant that we can cause it to go out with indirect methods like a tied plastic bag of water next to it, that melts, spills its contents and extinguishes the fire. But one must NOT be stringent in these matters, meaning, if there’s any doubt put out the fire!