Type F lacks certain "friction modifier" additives which were necessary for cars which specified Type A in the old days (superceded by the various Dexron/Mercon things) to shift smoothly. If you put Dexron in a transmission which needs Type F it will shift VERY smoothly, but burn out its clutches rather rapidly -- this is a very common problem nowadays for owners of classic SAAB 900 models and other older European cars with Borg-Warner type 35 and 37 transmissions: people substitute Dexron, thinking it's just an improvement, and shorten the life of their transmissions rather drastically. If, on the other hand, you put a large amount of Type F in a transmission intended for Type A or Dexron, as drag racers used to do all the time in the '60s, you just get much firmer shifting. I suspect that some of the cheaper "shift improvers" or "transmission performance improvers" in auto parts stores are just repackaged Type F.

I believe that the major factor in the change from Type A to Dexron designation was the invention of a synthetic friction modifier additive: Type A used genuine whale oil, and the limits on whale hunting made it difficult to obtain enough for all those GM cars.