"Save the world" is a subset of "improve the world" where saving is improving by a lot in a way that the world really needs it. "Improving the world" can mean settling for a smaller improvement, but probably doesn't mean "improving in every way so it will include saving the world". If people stop wanting to "save the world" because they weighted their desire to improve it in lesser ways anywhere near their desire to save it, to sound less egotistical, to avoid the applause light, or to dissociate from people who think they're saving the world by raising awareness or making a list of people who say they want to save the world, or whatever, and the world doesn't get saved because of it, I will be sad.