Glad you liked the demo! I was first a bit scared of showing off Termina because it was so different, but people seem to take it pretty well.
The same areas are in the full game too, but a lot of things have been added to them. From small details and new enemies to entirely new rooms and such. There are also alternate paths early on, so if you know how, or stumble upon them by accident, you can skip the demo sections too.
Don't transfer old saves. It will create a myriad of problems if you do so. I have no idea how the game would play with a save from the demo.