'morphism' originates from New Latin/Greek, specifically the Greek word 'morphē', where 'morph-' meant 'form' and the suffix '-ism' (via Latin/Neo-Latin) denoted a state or condition.

'morphē' passed into Neo-Latin and the scientific/International vocabulary (e.g. terms like 'morphosis'), and the English noun 'morphism' arose in scientific usage in the 19th century.

Initially it referred to 'form' or the process of forming; over time it came to mean 'a form' and in scientific contexts has specialized to mean 'structure' or, in mathematics, a 'structure-preserving mapping.'