It seems like you may have made a new Apple ID in order to make a new Game Center account:
"When you sign in to your iCloud account, a Game Center account is created for you (if it didn’t exist already). When you’re signed in to your iCloud account using the same Apple ID on all your Apple devices, your Game Center account is available on all the devices; any games you purchased using the same Apple ID are also available."
Maybe this article about trying to delete Apple ID will give you some idea of what is happening...