In the case of the F-111, the 'F' might stand for something else...
well, they are alot prettier than the f-4's, but give me a phantom anyday........
Like many USAF aircraft they were given the label F to impress Congress into more funding.
The F-111 would be more properly thought of as a light bomber.
It was designed to deliver nukes to the USSR while flying barely above tree top level.