The shade of difference between these virtual synonyms -- applicable to both persons and events -- is reflected in the Greek usage of the two verbs (epsilon 2674, sigma 1639, sigma 1648). This difference becomes more significant in the derivative nouns (see epsilon 1468, of meetings; sigma 1650, sigma 1638, of coincidences).
The entry derives from a scholion to Aristophanes, Birds 1493, that uses the present participles of the two verbs, the former governing h(/rwsi, as here. The note is based on a passage in the play (lines 1483-93) that also uses the two verbs, with particular reference to meeting a named hero, Orestes (web address 1).