'smooth-printed' is a compound in Modern English formed from 'smooth' and 'printed'. 'smooth' originates from Old English 'smōþ', where the root meant 'smooth, even'. 'print' (and 'printed') comes via Middle English 'printen' from Old French (e.g. 'preindre'), ultimately from Latin 'premere', where 'premere' meant 'to press'.

'smooth-printed' arose by combining the adjective 'smooth' + the past participle 'printed' in Early Modern/Modern English usage to describe the quality of a printed surface; the compound followed regular productive processes in English for adjective formation from past participles.

Initially the elements conveyed 'smooth' (surface quality) + 'pressed/printed' (from 'premere' → 'print'), and over time the compound came to mean specifically 'having a smooth printed finish' rather than a more literal 'pressed smoothly'.