"I'm going to" means you have decided/planned to do something. "I want to" means you would like to do it, but maybe you won't do it, or can't do it, etc. You haven't taken the steps to make the wish a reality. Example: "I want to go to that concert next month, but I don't know if I can afford the expensive ticket." "I'm going to that concert next month: my mother bought me the ticket!"

They are completely different, I guess.