Each domain is a separate server running a separate instance of the game. Resources and alliances cannot be shared between domains. Each player may play on more than one domain if they choose. Gems are the only currency that is shared on a player's account, between domains.
The designers have added code to prevent people from creating new accounts on the older servers. If you use these links, and you select a domain where you already have an account, it should take you right to it. If you do not have an account, and the domain is one of the many that are locked out, you will be assigned to a random "new" domain instead of the one that you selected.