'smooth' originates from Old English, specifically the word 'smōþ', where the root meant 'even' or 'without roughness'. 'bill' originates from Middle English, specifically the word 'bille', where it meant 'beak' or 'projecting piece'.

'smooth-billed' is a Modern English compound formed by combining 'smooth' with the past-participial/adjectival form of 'bill' to mean 'having a smooth bill'; this compounding pattern produced the fixed compound 'smooth-billed' in recent English usage.

Initially it simply described the two elements ('smooth' + 'having a bill'), and over time it has remained a literal descriptive compound meaning 'having a smooth beak'.