No, the World's Fair was where Walt tried out his concept for Disney World
I was only 5 or 6 for the fair, so my parents had to take me - but I still remember it vividly.
You really need to get yourself to Disney World to get on It's a Small World and Carousel of Progress - you will be brought right back to the World's Fair ^^
Oh, and they're still using that song for the ride. They changed it for a while, and now it's been returned to the original.