On the words וישמע יתרו Rashi asks: “What report did Yitro hear that he decided to come to Moshe?” Rashi answers קריעת ים סוף ומלחמת עמלק. However, Rashi comments on the words את כל אשר עשה אלקים למשה לישראל עמו that כל אשר עשה refers to the following three miracles: the Mann, the Be’er, and Amalek. Three difficulties emerge: Firstly, why is it necessary to learn the miracle of the victory against עמלק from two different phrases (ie. וישמע יתרו and כל אשר עשה). Secondly, why does Rashi describe the victory against עמלק first as מלחמת עמלק and then as simply עמלק? Finally, why are the miracles of קריעת ים סוף and מלחמת עמלק ascribed to וישמע יתרו and the miracles of the Be’er, Mann, and Amalek ascribed to כל אשר עשה; after all קריעת ים סוף and מלחמת עמלק were also miracles that “Hashem did”?
R’ David ben Shmuel Halevi Segal (author ofטורי זהב known as the Taz) answers as follows: ה' essentially performed two types of miracles in Egypt upon the exodus of the Jews from Egypt, and during the 40 years in the מדבר. The first type was a miracle that was essential for the survival of the Jews.
The Mann and Be’er are examples of this. Without food and water the Jews would have perished. These are the miracles that the Torah can describe asכל אשר עשה לישראל עמו because their purpose was for the Jews only. The second type of miracle was one whose primary objective was for Hashem to demonstrate His power and control over nature and all creatures. קריעת ים סוף is an example of this. After all, Hashem did not have to take the Jews to Israel through the Red Sea. This is what caught Yitro’s attention (וישמע יתרו) but cannot accurately be described as כל אשר עשה לישראל עמו since it’s objective was not primarily for Bnai Yisrael but rather for Hashem Himself to demonstrate to the entire world.
Regarding עמלק both objectives were employed. Obviously Hashem cold have directed the Jews on a different path and they could have totally avoided עמלק. However, since Hashem wanted to demonstrate His omnipotence, He orchestrated a מלחמת עמלק. In this fashion the world would realize that only ה' איש מלחמה. It is for this reason that Rashi uses the phrase מלחמת עמלק with קריאת ים סוף on the other hand once a war was waged the tired and weak Jewish nation required a miraculous (but essential) delivery from this overpowering nation of עמלק. This Rashi describes as simply עמלק ie. our salvation from עמלק.
In summary, it was the report of Hashem’s wondrous miracles that demonstrated His control over nature and all living beings (i.e. קריעת ים סוף and מלחמת עמלק) that brought Yitro to Moshe. It was the essential miracles of our salvation from עמלק the באר and the מן that are accurately described as כל אשר עשה ה' למשה ולישראל עמו.