逢う is often used for close friends, etc. and may be associated with drama or pathos; 遭う may have an undesirable nuance

to meet; to encounter; to see

Word usually written using kana alone; Esp. 遭う when in kanji

to have an accident; to have a bad experience

Common noun; Adjectival nouns or quasi-adjectives (keiyodoshi); Nouns which may take the genitive case particle 'no'

coincidence; chance; accident; fortuity

Adverb (fukushi)

by chance; unexpectedly; accidentally

Common noun; Philosophy

contingency

encounter; running into; meeting with (e.g. an accident); being confronted with (e.g. a difficulty)

one's circumstances; environment; situation (in life)

遇う only

to treat; to handle; to deal with

to arrange; to decorate; to dress; to garnish

Noun, used as a suffix

treatment; reception; service

working conditions; salary; pay; remuneration

unexpected meeting; coincidence

treatment (of a person); dealing with

favorable treatment; favourable treatment; hospitality; warm reception; good treatment; hearty welcome

to have a bad time; to go through a bitter experience; to get into trouble; to get hurt; to suffer