"cannot" vs. "must not"

Solution 1:

Yes a big difference.

Cannot die means the person is immortal and incapable of death.

Must not die means that they are mortal, thus very capable of death and the mission requires you to keep them alive.

Solution 2:

In this setting they are pretty much the same. Language can have a literal meaning, a canonical meaning (the first thing you think of), a metaphorical meaning ("the face of a cliff"), and implied meanings.

Literally, "cannot" means logically or physically impossible: "we cannot pick up that huge boulder". And "must not" means not allowed. But both here are said in order to convey that, loosely, you really don't want to let person X die and you should try tomake that not happen. So they're pretty similar here.