I know the query is addressed to
@sudoer but I just jumped in to save his time. Hope
@sudoer wouldn't mind.
THC stands for The Hotel Collection, which is an exclusive hotel booking option on selected hotels for Platinum Charge/Centurion and Reserve Credit Cards members (not sure if this has been extended to other "higher end" Amex credit cards. For bookings of a minimum 2 nights and comes with various benefits like US$100 food/property credits per stay/booking, possible room upgrade (subject to availability), etc. but NO breakfasts included. Normally, your hotel membership benefits would be recognised (though unlikely double dip on room upgrade, etc.)
FHR stands for Fine Hotels and Resorts. A booking option exclusive for Platinum/Centurion Charge Cardmembers. Can book a single night on hotels in the program. US$100 food/property credits per stay/booking, usual status benefits like room upgrade (when available), guaranteed late check-out until 4pm, etc. Recognition of hotel membership for loyalty bonus (points and status credits/nights) is quite pertinent.