• Collect the server status that FFXIV reports for its own servers.
• Ping all game servers (lobby and game servers).
• Check open ports on game servers (aka: portscan the game servers).

Knowing which game server is running on a given IP/port is extremely time-consuming to figure out (the IPs change regularly). So instead I split up the 2 pages to present you the information gathered to let you figure out if there is a possible problem with your server. Though, a datacenter (Aether, Choas, etc...) tend to all go down at once.

• Login Server: This is where you type in your username/password to get a token to connect to the Gate Server.
• Gate Server: Reports the status of the servers to the launcher. Plus shows the login message before entering the game.
• Lobby Server: There is one lobby server per Logical DataCenter. This is where you do character selection and connect to a realm (it directs the client what the ip/port of the game server is). It also reports queue information to your client.
• Game Server: Now adays the server you connect to, to play FFXIV is just load balancers to the actual game servers behind the scenes. It's why you can visit any other realm in a region: all the servers are likely all next to one another, and there is mainly just logical separation between eachother.

Back before Final Fantasy XIV launched, I ran a fansite called ff14news.com (archive.org snapshot of the site), which had a server status tracker for it. After being heavily disappointed in the original release of the game, I disappeared.