Originally, G meant wide angle twincam (45deg) and F means narrow angle twincam (22.5deg).
This led to the whole performance vs economy, as historically speaking, FE heads were generally on more conservative motors. (1ZZFE vs 2ZZGE etc)
But a few people are now claiming that the narrow angle heads have more potential (I think F1 engines have a very narrow angle).
The other trains of thought are that G heads are heads designed by Yamaha, and F heads are Toyota designed heads.
Or possibly G heads have individual cam sprockets, were as F heads have only one cam sprocket, with the exhaust cam driven off the intake cam (or viceversa)