According to Mark Cerny, PS5 Pro's PSSR will come closer to the FSR 4

AMD and Sony have collaborated on the Amethyst project, an initiative aimed at developing graphics technologies for PCs, mobiles and consoles. The PlayStation 5 Pro, based on a hybrid architecture combining RDNA 2, RDNA 4 and a unit dedicated to machine learning, will incorporate a modified version of FSR 4, again under the name PSSR.
Mark Cerny confirmed to EuroGamer that PSSR will evolve towards an algorithm similar to FSR 4, but adapted to the console’s specificities. This system should be ready for games scheduled for 2026. He pointed out that optimizing for stable frame rates is a priority on consoles, unlike PC GPUs. Before fully integrating machine learning into PSSR, Sony plans to extend its compatibility to more games.