'non-equivalence' originates from Modern English as a compound of the prefix 'non-' and the noun 'equivalence'. The prefix 'non-' ultimately comes from Latin 'non', meaning 'not', and 'equivalence' derives from Latin 'aequivalentia' (via Old French/Medieval Latin), where 'aequi-' meant 'equal' and 'valere' meant 'to be worth or have value'.

'equivalence' changed from Latin 'aequivalentia' into Medieval/Old French forms and then into Middle English 'equivalence'; the negative prefix 'non-' has been used in English since Old/Middle English as a borrowing from Latin/Old French. The modern compound 'non-equivalence' is a relatively recent formation in technical and academic English, combining these elements to express a negative state.

Initially the components denoted 'not' and 'equal in value'; over time the compound has come to be used broadly in mathematics, logic, translation studies, and other fields to mean a general 'lack of equivalence' rather than a narrow monetary or value-based inequality.