I played all the way through the demo. The screen says, "This is where the demo ends. You can save the game now so you can resume playing from here." I purchased the full version using the link in the Start Menu of the demo. My saved games from the demo do not show up in the full version when I try to load them.
I purchased the demo from Google Play last weekend. When I clicked the "Buy Now" from the demo Start Menu, I chose the Google Play option. The full version downloaded, and it opens fine. I have both icons on the screen. Both start just fine. The Full Version does not have any saved games for me to load.