Does "live on" here mean something like "exist"? If not, what's the difference?

Rebecca

It's similar! If something "lives on," it continues to "exist." Something can "exist" and be "alive," but for something to "live on," it continues to exist into the future in some kind of form. Ex: He hopes his family name will live on for many more generations. Ex: Even if I fail this time, my dreams will still live on, and I'll try again.