Conceptual difference means that two words or attributes express different intelligible contents. Existential separation means that one can exist independently without the other.
“Knowledge” and “power” have distinguishable meanings. Yet one does not posit that divine knowledge exists without divine power at some time, or that they are two separate independent deities.
Many apparent difficulties about “neither identical nor other” disappear once conceptual equivalence and separability in existence are assessed as different claims.