It's a long story but basically electrorefining and the Silex...

It's a long story but basically electrorefining and the Silex process do different things.

Electrorefining is a process derived from what the old EBR-II (see HERE) and was picked up by GEH to complement their PRISM reactors which as I understand it has now been superseded by the Natrium reactor now in co-operation with Terrapower (Bill Gates sponsored). The main characteristic of both the Natrium (and PRISM) and the Oklo reactor is that they are all "fast" reactors; meaning that they operate with "fast" neutrons rather than slowed down (or "thermal") neutrons Most other reactors are "thermal" reactors which have a long track record. A big advantage of a "fast" reactor is that it is far less "fussy" about it's fuel than a "thermal" reactor (the other advantage of a "fast" reactors is that it can be designed to "breed" fuel (although the Natrium doesn't do that). Electrorefining is an electrolysis process in molten salts (similar to aluminum smelting) which separates "fission" products (those produced when a U235/Pu239 atom splits), uranium (RepU) and "higher actinides" (Pu,Np et al with atomic number greater than 92). A "fast" reactor can continue to fission "higher actinides" and also RepU provided the RepU has sufficient U235 (or Pu239/U233) added to it (that's a role for HALEU) o continue fission. A major issue with RepU is that as it fission's about 85% of the U235 atoms spli and produce energy bu 15% transmute to U236 which in a thermal reactor act as a poison which has to be compensated for by blending with HALEU (the Russians call this REMIX). As the used RepU is recycled in a thermal reactor it needs progressively more U235 to compensate for the U236 (poison) in the RepU. A "fast" reactor (such as Natrium & Oklo) is far less sensitive to U236 - it will fission with "fast" neutrons and provide energy (as also will the "higher" actinides).
However "fast" reactors have their problems (i.e. little experience, cost, sodium (inflammable) coolant and worst a positive void coefficient - like Chernobyl (as the temperature rises so also does the reactivity). Hopefully new designs (e.g Natrium/Oklo) can mitigate "fast" reactors inherent problems. The DoE have continued electro-refining at Idaho National lab - INL) with EBR-II spent fuel from prior to 1993 (see HERE) and also used military HEU fuel (from submarine and aircraft carrier reactors) - they intend to use some of this (blended) as early HALEU, however "thermal" SMR suppliers are unhappy to use this HALEU since it will contain U236 (a poison for thermal reactors)

The Silex process is different in that it takes one element (e.g uranium/silicon) and ONLY one element and separates it into its isotopes (i.e same element (number of protons) but different atomic mass (number of neutrons) - it is not used to separate elements. Where the Silex process is uniquely useful is that it can potentially remove the U236 from RepU (centrifuge cannot do this). However to do this the RepU still needs to be separated from the used fuel (possibly using electro-refining or chemical methods) and then converting to UF6. A problem with UF6 from RepU is that it will be radio-active (or at least more so than natural uranium or uranium tails) and will need "special" handling in the Silex process (i.e done in a glove box or worse a hot cell).

In summary the processes do different things - Silex is important for "enrichment" of isotopes, electro-refining is for "separation" of elements .