What is the difference between "v'Lo Sechal'lu" and "v'Nikdashti"?
See Sifsei Chachamim.
Rashi: With the express intention of dying, which is subject to a miraculous salvation - as occurred to Chananyah, Misha'el and Azaryah (See Daniel, 3:8). Not like Haran, who allowed himself to be cast into the furnace and died, because he thought that, like his brother Avram, he would be saved (See Rashi, Bereishis 22:28).
Why does the Torah add "be'Soch Bnei Yisrael"?
Rashi: Because it is only in public 1 that one is obligated to give up one's life.
Seforno: Hashem is sanctified among Yisrael when He performs wonders with them, when He rules over them directly, without a medium. 2