What is the difference between "Motzo'eihem" and "Mas'eihem"?
Rashi (in Mas'ei Sh'mos, 40:38) and Rashbam: "Motzo'eihem" means 'the places where they encamped' ('their encampments' ? Rashbam) and "Mas'eihem" 'their travels.' 1
Seforno: "Motzo'eihem" means the place that they departed from, and "Mas'eihem", their destination.
Oznayim la'Torah: "Motzo'eihem" means things that happened to them, and "Mas'eihem", implies that Moshe transcribed the events that occurred after the termination of each journey. 2
Why does the Torah insert "be'Yad Moshe ve'Aharon"?
Targum Yonasan: It is referring to the miracles that Moshe and Aharon performed during their travels in the desert.
Why does the Pasuk switch "Motzo'eihem" and "Mas'eihem"?
Seforno 1 : Because sometimes their destination was a bad one, whereas the place that they had left was good, 2 and sometimes the opposite was the case. 3
Oznayim la'Torah #1 Although Moshe transcribed the events that took place on each journey, here, he mentioned the journeys, and by mentioning the journey, the reader remembers what happened there - for better or for worse. 4
Oznayim la'Torah #2: "Motzo'eihem le'Mas'eihem al-Pi Hashem" refers to where they journeyed by Divine instruction to travel from Egypt to Eretz Cana'an, whereas "Mas'eihem le'Motzo'eihem" refers to where they lost faith and traveled back towards Egypt. 5