= Solution
The distinction is between \b[partitioning reusable fuel constituents from fission-product waste], and subsequently \b[partitioning <uranium> from <plutonium>]. In the first operation, chemical selectivity transfers selected <actinides> into a different stream while most <fission products> remain in the waste stream. In the second, differences in <chemical speciation> allow the two recovered elements to follow different streams. Neither operation separates <uranium> <isotopes>: <uranium enrichment> and chemical element separation are different tasks.
At a conceptual level, <solvent extraction> exploits unequal affinities of dissolved species for immiscible liquid phases. <complexation> changes those affinities, while a change in <oxidation state> can change an element's preferred phase without changing its identity. This explains why a stream bearing <actinides> can first be separated from much of its accompanying waste, and why <uranium> and <plutonium> need not subsequently remain together. Dissolved and undissolved residues, contaminated solvents and off-gases remain waste-management obligations; a recovery percentage alone is not a complete material balance.
Equipment must provide phase contact and phase disengagement within shielded, confined systems. Remotely maintained contactors and settlers are equipment categories serving those functions; sealed transfer systems, shielded cells and monitored off-gas handling limit contamination and exposure. Cooling manages residual <decay heat>, and <nuclear material accountancy> follows inventories and losses. <criticality control in radioactive waste> is essential because <solvent extraction> can redistribute fissile constituents. \b[Scoped limitation:] this answer gives the chemical principles and equipment functions; operational fissile-separation recipes, reagent sequences, contactor design details and process conditions are intentionally not supplied.
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