not necessarily, fsr 1.0 did not use the LOD system at all. it directly drops EVERYTHING to the rendered resolution and applies a sharpening filterFSR and FSR 2.0 use the same LOD system. All these upscalers, require adjustment to LODs.
The difference is the use of temporal information by FSR 2, DLSS 2, XeSS, TAAU and TSR,
FSR 1.0 can be literally used as a post process filter by RPCS3, Xenia, emulators, many more software etc. Engine level FSR is no different than post process FSR. It simply does nothing with engine itself. Its just a simple way of reducing the resolution directly as if you're choosing a lower resolution and apply a sharpening filter.
you can go find any fsr 1 and fsr 2 game (there are some) do comparisons between lods both respectively at quality settings and you will quickly realize this is true