What's the difference between i.e. and e.g.?
c.1300, perhaps from Middle Low German *smilen or a Scandinavian source (e.g. Danish smile "smile," Swedish smila "smile, smirk, simper, fawn"), from Proto-Germanic *smil-, extended form of PIE root *smei- "to laugh, smile" (cf. Old English smerian "to laugh at, scorn," Old High German smieron "to smile," Latin mirus "wonderful," mirari "to wonder"). Related: Smiled; smiling.
Gradually pushed the usual Old English word, smearcian (modern smirk), into a specific, unpleasant sense. Of the eyes, from 1759. Figuratively, as indicating favor or encouragement, from c.1400. Romance, Celtic, and Slavic languages tend to use a diminutive of the word for "laugh" to mean "smile" (e.g. Latin ridere "laugh;" subridere "smile"), perhaps literally "small laugh" or "low laugh."
1560s, from smile (v.).