The P47 was originally designed as a fighter for what these days we'd call the Air superiority role and interceptor roles. That is, defeating the enemy fighter force and destroying their bombers. This is why Republic fitted it with the biggest engine/turbo-Supercharger setup they could use (to make it fast and good at altitude) and a heavy armament (to do maximum damage).

And it was indeed successful at this - to a point.

While the Thunderbolt had a good range it still wasn't enough to escort bombers all the way into Germany so when the Merlin engined P51 became available the P47 was gradually moved into other roles .

By a happy accident the P47 turned out to be perfect for the fighter-bomber role. The air-cooled engine could take damage that would bring down a Spitfire or P51, the mass of ducting in the fuselage and the sheer size of the aircraft protected the pilot from harm - there's a joke that P47 pilots could dodge enemy fire by running around inside their cockpit - and 8 x 0.50in machine guns could do horrible things to ..basically anything short of a tank.

Add in bombs and rockets and you had something that could smash up a German column quite nicely.

(As an aside, the P47 can be seen a development of the earlier P43 Lancer which was always intended as a pure fighter.)

As a follow up: are there any online resources that list the formal aircraft specifications issued by the Army Air Corp and the Navy before and during WW2?

Edit: in particular, it seems that the XP-47 was designed around the specifications in Circular Proposal 39-770. Is the text of this proposal anywhere online?

Since the P-47 had been covered well, the F4U was originally designed as an air superiority fighter. While Japanese bombers were fairly prevalent on larger islands and mainland China, they had limited use in the relatively small airfields on the Pacific and limited effect versus the entrenchments between islands. Obviously torpedo bombers and dive bombers were far more practical in the Pacific theater.

The F4U and F6F both came around the time that the Navy realized their planes were awfully outdated, those being the TBF dive bomber, the F2A Buffalo, and the F4F Wildcat, all of which performed exceptionally poorly against A6M5s during Pearl Harbor.

The F4U which was already in development continued with the American tradition of speed > maneuverability in a fighter because the US realized fairly early on that the pilot with speed dictates the engagement. So coincidentally the F4U was designed as a naval fighter, which means it has to have a reasonable climbrate to get itself to an acceptable altitude in reasonable time, as well as being the traditional US fighter which emphasizes speed and firepower. These characteristics did make it suited to shooting down bombers, however it never really had that much of a need. Nothing like the Spitfires were during the Battle of Britain or the Fw 190s were during the mainland ETO.

Once the US established air superiority by practically obliterating the majority of Japan's pacific air fleet and carriers to the point where almost all fighters were then held on reserve on mainland Japan in the event of what the Japanese saw as an inevitable invasion, the F4U shifted towards a ground attacker roll as the plane was exceptionally sturdy which worked well for mounting hardpoints for ordinance.

Fun fact: The F4U is one of 2 propeller planes to shoot down a jet over Korea. One being an F4U-4 engaging a MiG-15 and the other being a Sea Fury engaging the same