Q. Lead designer vs. Director - is there really a difference?
A. Not really although a Director should have more responsiblities beyond the design of the game.
Q. Secondly, is shooting for lead designer too high of a goal?
A. No as long as you understand that it cannot be your first step in the industry. Start somewhere lower down and work up.
Q. What sort of field, other than game design, should I aim for if I wanted to get into lead design? Would these be possible through a JC?
A. Tough question. I can't answer it as 'Game Designer' education is questionable at the best of times. Consider reading Sloperama: http://www.sloperama.com/advice.html
Q. I just want to create, unique, memorable worlds and stories. Of course this would tie with fun gameplay, with unique elements to that world. Is there any way to apply this to a certain field of education?
A. What is stopping you making them now?