MAP is Manifold Air Pressure. If it is not reading properly there will more than likely be poor engine performance, and perhaps be accompanied by black smoke. If the Engine Controller can not read Air Pressure, it could continue to dump fuel into the cylinders until if sees something. There are boost "foolers' that do similar things, but still leave your truck drivable.
Never had a APPS wiring problem, but I have adjusted mine recently, and have fooled it as well.
Is it possible to replace APPS and not erase the code and have still problems because you didnt erase the codes. Im shooting two codes and one was the map and the other is the Apps. So I replaced the APPS and problem still same. Limp mode throttle jumpy dead pedle. Then the throttle kicks in and out. even seems to stick a little once letting off. Totally stumped.
start with checking and cleaning all of the grounds. And you said you did replace the apps but the problem still exists and that clearing the codes they come back right away. Are you clearing the codes with a scan tool or disconecting the batts? If you are using a scan tool that should clear the hard fault codes but just disconecting the batts will not anyways if they do clear and comeback i would check all of the grounds and all of your connectors to the map, apps any bulk head connectors and the connectors at the pcm try that and see what happens.
seems like your map senser isnt pluged in all the way thats what my truck did when i had the same problem check there mine clicked and locked and everuything just need a little bit more for the full connection