Why is Shabat haGadol celebrated based on day of the week (Shabat) and not day of the month, if it happened on the 10th of Nissan? Most other days of commemoration in Judaism are celebrated by a day of the month, and not "day of the week relative to a date." What makes this one different?
According to chabad.org
"A further reason why we recall the miracle on Shabbat rather than on the tenth of the month is that, forty years later, Miriam died on that day and the well which accompanied the Children of Israel and provided them with water in the wilderness, disappeared. When the anniversary of Miriam's death fails on a weekday, some observe it as a fast for the righteous."
The Chasam Sofer gives the following explanation (I heard this quoted, don't know where to find it) for why it is called Shabbos HaGadol. Every Motzai Shabbos we say ויהי נועם to lengthen the return of the souls that were released from Gehinnom for Shabbos who must go back on Motzai Shabbos (Tur O.C. 295). However, when Yom Tov is during the week, we don't say it, because the souls are not returned to Gehinnom for such a short period since they will be coming back in less than a week, when Yom Tov arrives. Therefore, the extra soul of Shabbos remains for the week, and the sanctity of Shabbos is thereby extended into the week. The first time this happened was the Shabbos immediately before the first Pesach. In commemoration of this "big" Shabbos, we call it "Shabbos HaGadol."
This would explain why it is a title unique to the Shabbos, not to the date.