I'm trying to move my world from my Linux install to my Windows install, and it's not working. I delete the "My Games/Terraria" folder from Windows, and copy over the one from Linux, but when I start up Terraria on Windows and load the world, it's still the old one. The one I deleted. I have no idea how this is happening.
The world is most likely in the cloud. When you move a world or a character to cloud in the Terraria interface, is literally moving it, not making a copy, your world resides in the cloud, and it takes precedence over anything local.
Now you're saying that when creating new worlds, they're both the same; so there might be a problem with your worlds being automatically moved to cloud once created.
You can disable the cloud storage per world, by clicking on the little cloud icon alongside each world and character, or you can disable cloud storage globally for the game by going into the game properties from steam and disable the cloud storage. Also if you want, you can re-enable it once your worlds are where they're supposed to be.