It means you now have a separate park. You can switch between them via the settings button ‘switch park.’ You will not lose your progress nor will it mess with any account connections (I don’t think). You may get some errors when switching parks but it hasn’t been anything progress altering. It’s usually presented with a text box saying something like “Uh oh. There’s something wrong. We’ll cast a spell and reload the game” and everything is fine
If you befriend your other game(s), you can give yourself a gem from that game. If you collect enough ice berries, you can get Goody's sugar shack and give yourself food along with the gem. If you confine your habitats to a single island, it will always be easy to find the three party hats in your other game.