Is there a difference between saving the planet and saving the world. I think so. George Carlin speaks of the pointlessness of saving the planet.
There is a big philosophical question as to whether it is “my world” or “the world”, but from my perspective it only exists for me because I exist.
Either way, the plan doesn’t change, spend time energy and money saving “my world” or “the world” amounts to the same thing, resulting in the same actions.