Can't speak about the field aspects of
GNAS – I'll leave that to those more qualified.
The EFAA came about in East Anglia, and was linked to the NFAA in the USA (something to do with large amounts of US service personnel in East Anglia). Their influence was what drove things towards marked distances. At the time there was also a BFAA (British Field Archery Association), but this merged with the EFAA in the early 70's, due to the International body, the IFAA, only recognising one organisation per country.
NFAS came about out of the EFAA in about 1972. I think it had something to do with classes and arrows.
The
NFAS is probably the largest of the Field organisations.