F is only used on fords and it is the F from Ford. F marks were put on GPWs because Ford wanted a way of singling ford parts from Willys ones.
From what i think, most people refer Jeeps to Willys but Ford wanted a way of showing that they were in it too and they can prove it by showing the F mark.
F parts can make a small fortune on Ebay, but beware, not all F stuff is genuine even repros are made with Fs and i have seen F stamps for sale so just be careful.
We are lucky that our jeep consists of mainly original parts which are F marked. Not many were visible at first but we are still uncovering quite a few every now and then.