I recently watched an old episode of "Dogfights!" from the History Channel. I noticed that the F6F Hellcat (and previous models) were strikingly similar to the P47 Thunderbolt. I went on google to see if I could find any information that correlated to the sharing of aircraft design between the military branches during the war, but could not find anything.
Was the AAC P47 Thunderbolt design the inspiration behind the Navy F6F Hellcat? If so, were there any other planes that shared a design but were deployed by a different branch either in a different role, or modified for a different role?
While I couldn't say to a specific sharing of designs between either aircraft manufacturers or designers, the main 'design scope' you are seeing between the hellcat and thunderbolt is just the accepted overall design of radial air cooled engine equipped aircraft. A large radial (often in US planes a double wasp) engine, in this case between the F6F and P47 it's the same engine, with the aircraft body and cockpit built around it, two wings, and tail section
For single seat fighter aircraft you basically had two engine types. First, Large radial air cooled engines (RAC). Like the Hellcat, Thunderbolt, Corsair, Dauntless, Zero, Fock Wulf 190, and so on. And second, slimmer liquid cooled engines (LCE), usually in a V piston configuration. Like the Mustang, Spitfire, Hurricane, BF 109, Warhawke, and such.
The differences between to two 'types' of aircraft fell essentially to their role and need. LCE planes were lighter, more streamlined, often had higher top speeds and higher flight ceilings, more agile and maneuverable, all of which led them to the preferred role of dogfighter (for the Europe campain*) and bomber escort. RAC aircraft however where much more robust and durable, had a higher horsepower rating with most RAC craft producing at or in excess of 2,000hp, where the LCE planes even at their individual zenith models only put out around 1,400-1,700 horsepower.
The performance differences related to task/needs can be seen in the P47 Thunderbolt itself. Originally used to escort allied bombers out of England, it had a greater success as a ground attack plane as both it's engine could take a greater amount of enemy fire, and it's larger size could include a larger amount of cockpit/pilot armouring than for example the P51 Mustang, which took over the escort/fighter roll.
This is why there were essentially no LCE aircraft used as carrier based planes in the Pacific Campaign. The robust nature of radial engine aircraft lead them to the better choice over the water, they could take a greater beating than their liquid cooled counterparts, and offered a greater chance for the pilot to return to what was often a single return point: their carrier or island landing strip. That is why I asterisked 'european campaign' earlier, flying over land has the obviously increased pilot survivability of aircraft loss because you can bail out and walk way.