The origins of the P-51 are pretty interesting in its own right. The early iterations the Mustang Mk I and II was initially conceived as a way to plug in the lack of supply of P-40 Tomahawks due to Lend Lease over-stretching the Curtiss-Wright plant.

Though the original lacked an engine that could operate at higher altitudes due to the Single Stage Supercharger on the Allison V1710 the Mustang's advantage was that it had a much longer range and a very high fuel capacity as well as excellent handling characteristics under load. Even with the ceiling of around 12,000ft the Mustang Mk I and II were still exceptional low altitude and ground Reconnaissance planes that the RAF used well into 1945 for the purposes of close air support and low-altitude reconnaissance .

On the American side the Allison based Mustang was also considered for bomber escort purposes due to it's exceptional range. Noting the Allison's lack of high altitude performance, the USAAF decided on the P-51B, a modified Mustang X with a Merlin 61 twin-stage Supercharger giving it not only more power, but a higher operational ceiling than the original P-51A/Mustang Mk I based off of the Allison V1710. But as the Merlin based Mustang began introduction it was clear that the Mustang's range far exceeded the P-47's or the P-38's range and by 1944 the P-51D began to overtake the P-47 and P-38 in bomber escort service relegating the other two to ground attack and closer range missions.

To answer the second part of your question, the P-47's dominance still continued on the ground and in lower altitude engagements. Much to the pleasure of allied air commanders, the P-47's exceptional carrying capacity made it an excellent fighter bomber after it's role as escort fighter receded with the introduction of the P-51B and D. Likewise the P-38 saw massive success in the Pacific theater until the introduction of the Merlin based P-51 and still saw continual success as a long range fighter as well as a fighter bomber well into 1944.

The early P-51s frankly still suffer from an interesting case of underexposure but that's mainly because most of the P-51A use cases were under the RAF as support fighters. Interestingly the lack of high altitude performance was never a surprise to RAF engineers who understood the capabilities of the Allison so it's actually rather curious why people have constantly underrated the P-51As considering it has least numbers of all the Mustang types in mass production.