"Berlinetta just means "coupe." It is not comparable to "Modena," Maranello," "Scaglietti," "Fiorano" etc. One could also bring up "Spider" as counterexample. But it isn't.
Of course, Ferrari really cheated using "GTS" with "S" for "spider" on cars like my 328 with removable hardtops. The term "spider" properly only refers to cars with soft tops as on the later models. But then, they couldn't use the term "targa" because that is, as I understand it, copyrighted by Porsche.
I believe FF stands for Ferrari Four and the "Four" stands for Four Wheel Drive as this is their first 4wd for the street. Ferrari has made several 4 seaters.