It's complicated, but there are significant differences among fast, epithermal and thermal reactors with respect to the fuel type, fuel geometry (fuel rods and fuel assembly), cladding design and materials, coolant (or heat transfer medium). Between the fuel and cladding, one has to limit fuel-cladding chemical interaction, while between cladding and coolant, one has to limit the cladding-coolant chemical interaction (e.g., corrosion). There are the matters of neutronics, reactivity control, power/burnup distribution and response of the fuel and core to reactivity and coolant transients. Generally, fast reactors use smaller fuel rods (smaller diameter) than CANDU/RBMK/LWRs, and most fast reactors are cooled with liquid metal; one does not simply take a fuel rods from one type of reactor and place it in another.
BWRs do use spectral shift, in which increased voiding in the upper part of the assembly is accomplished by reducing the flow. With a slightly harder spectrum, one transmutes more of the U-238 to Pu-239, and then burns the Pu-239. Utilities would use spectral shift to reduce feed enrichment.
Fast reactor fuel lattices are triangular or hexagonal lattices, which are tighter than square lattices typically used in LWR fuel. Cooling and thermal limits on heat flux are considerations.
Fast reactors typically use enrichments of about 20%, or slightly higher, in UO
2 or (U,Pu)O
2, while thermal reactors (LWRs) typically use enrichments less than 5%, although slightly greater enrichments are possible. CANDU have used U of natural enrichments, but some more recent designs have used slightly greater enrichment. CANDU and LWR fuel can use different enrichments in different fuel rods, and different enrichments in different fuel assemblies (split batches).
Another key factor is burnup and it's limits as it relates the production of fission gases, so rod internal pressure is an issue, as well as transient behavior. In addition to the gases, burnup accumulation causes the fuel to swell, and fission products compete with the fuel atoms for available neutrons. U-233 produces slightly more neutrons (on average) per neutron absorbed than U-235 (and a lower capture cross section), enough to permit a thermal breeder. U-233 is not natural, but is produced through the transmutation of Th-232 -> Th-233 -> Pa-233 -> U-233.
https://iopscience.iop.org/article/10.1088/1742-6596/1689/1/012031/pdf