In the first game, if you die, you have to start the scenario from the beginning, saving is just if you want to quit the game, but your file is deleted when you reload it.
In file 2 if you die you can start back where you saved, this means you can save not too long before the Nyx fight, which makes it much, much easier and thank goodness for that because the Nyx fight is tough, I managed to beat Thanatos on my first try, but Nyx took me a handful of tries, it'd be close to impossible if the game expected you to start over from the beginning if you died fighting Nyx.