Here is my view and a small timeline:
- FSR 1 (Jun 2021): Post processing. Can be used with any game, any graphics card on any system. Quality is not very good, but developers do not need to support it in order being usable.
- FSR 2 (Mar 2022): Analytical and Game specific. Analyzes the content of the ingame in order to produce better output than FSR 1. Can be used only with games that have integrated support for. Still system and graphics card agnostic.
- FSR 3 (Sep 2023): Improved version of FSR 2. Therefore the previous point applies here too, but has a bit more features and should produce better quality. It was late on arrival and was controversial at launch.
- FSR 4 (maybe 2025): AI and hardware dependent. Not much is known, but we can expect that it requires some form of AI chip on the GPU. We don't know if it will be usable with other GPUs that have such a chip or is restricted to AMD cards. As this is analytical, it requires games to support this, therefore its Game specific as well. It's expected to have superior quality over FSR 3, maybe rivaling XESS or even DSR. But it seems the focus is on low powered weaker hardware, where it would benefit the most.