People like Aeris and Zack die of realistic causes because battle logic simply does not carry over into cutscenes. That's why Tidus in FFX can run down a walkway fighting soldiers and getting sprayed in the face with bullets without a scratch to show for it, then be stopped in his tracks as the scene enters a cutscene and guns are held to his face.

Cloud didn't die when he was stabbed with Masamune because that whole scene was set up to demonstrate how incredibly stronger Cloud is than Sephiroth. Plus, he's The Hero™.