Living is having a purpose and be able to spread around your talents, have dream, goals, feelings, etc. Existing is just being born in this world with no purpose, dreams, goals, emotions, etc. Kinda like just 'floating by'.
Existing: It's real, but not necessarily alive. Ты can prove that it's there. For example, a chair. A chair is an actual thing. Ты can prove they're real and they exist. Yes, they're inanimate, but they were invented and are used every single day. The Easter Bunny is an example of something that doesn't exist. He's a legend. Ты can't prove he's real. Basically, existing is being there, but not always having to be alive.
Living means that Ты have a purpose или goal in life if Ты will,you aren't just waking up everyday going through the motions,you feel fulfilled. Existing on the other hand,is when Ты just wake up and Ты are still breathing,you HAVE no purpose,you have no desires to fulfill,you have no wants to strive for. You're basically just there. And it can be by choice или in your lot in life but it's very hard to transition from existing to living. Especially for people who have a repetitive routine,everyday is the same,get up,go to work,come home, go to sleep. Wash,rinse,repeat! It's a vicious cycle sometimes,and believe me I feel that way some times! So I know! There's better ways to "live" so all I can say is never give up.