Hi,
It's nothing to do with hacking 🙂
The session shows up as the name "Mac OS X Internet Account" because iOS and MacOS use the same frameworks for internet accounts, so Facebook detects it as MacOS framework.
The active session is likely the one you set up in your iPhone 5C settings, to allow system-wide Facebook sharing and posting. If you wish to delete the account from your iPhone, simply go to Settings, then scroll down to the 7th group of options (containing "Twitter", "Facebook", "Flickr" and "Vimeo") and select Facebook.
- If it shows a Username and Password fields, it means the "Mac OS X Internet Account" session showing up on the Facebook website is not up-to-date (it sometimes happens if you reset your iPhone without disconnecting from Facebook in Settings). If you haven't reset your iPhone recently, you have likely logged-in to Facebook on some other Apple device (in a store, on Macdonad's iPads, etc), and it would be wise to change your Facebook password.
- If it shows other options ("Settings", "<yourname>", "authorize apps to use your account"), tap on your name, then tap "disconnect".
Regarding the IP address, you need to be aware that it is possible for different people to have the same IP address (especially on 3G/4G, rarer for Wifi). For instance, in France, I have the same IP address on the cellular network as all other customers of "Free", my cellular provider, which is located in Paris, at the location of the cellular provider's servers. An internet IP is not always unique.
That's it !
James