I'm guessing the other site is Seatguru or Seatplans. Be sure to verify the info you get on them as they're not know for being reliable.
What does AA.com say is the equipment on your day? I did some random dates and saw their 772 which has international business in the front as your "F" class which is something you should be happy with. This corresponds with this version on Seatguru.
https://www.seatguru.com/airlines/Am..._777-200_C.php or the 37 business class seat version on AA's fleet page.
Domestic F on internationally configured planes generally defaults to International Business. This doesn't mean the service will be International Business standards but you'll get a good seat & entertainment and sometimes a little upgraded meal.
Enjoy the flight.