Those P-47's were being ferried to their newly seized bases in the Marianas (as I guess it says). There was no intention for them to land back on the carrier, just be catapulted off and land ashore.
P-39's also did this, in the Pacific, in addition to P-40's as already mentioned. When P-40's were ferried across the Atlantic on the carrier Ranger on a few occasions, they flew off, IOW were not catapulted, similarly to the 700+ Hurricanes and Spitfires flown off to Malta in 1940-42 from RN, and on 2 occasions USN (USS Wasp), carriers. In a tiny handful of those cases a/c with mechanical trouble did manage to land back aboard, a Spitfire did so on one of the Wasp missions.
Late in the war the USN conducted landing trials with PBJ's (ie B-25's) on carriers. Catapulting or flying off from carriers was feasible for a broad range of WWII a/c not designed for it. Landing was harder but also feasible in a one-off emergency or trial in fairly many cases, especially on a bigger carrier. Day in/day out carrier operations with a reasonably low operational loss rate is where the purpose designed carrier plane usually had the advantage. Even somewhat successful carrier planes adapted from land planes were sometimes weak in that aspect. Needless to say the *pilots* also had to have carrier landing training; there was no attempt to do that in any of the USAAF ferry/fly off operations, usually minimal training even in the taking off part, but it usually went OK anyway.
Joe