run across vs encounter

run across is not a noun while encounter is a noun.

Word	Noun	Adjective	Verb	Adverb
run across	No	No	Yes	No
encounter	Yes	No	Yes	No

As verbs, run across and encounter are synonyms defined as:

Other synonyms of run across include come across, meet, run into, see.

run across (noun)	encounter (noun)
	a minor short-term fight
	a casual meeting with a person or thing
	a hostile disagreement face-to-face
	a casual or unexpected convergence

run across (verb)	encounter (verb)
come together	contend against an opponent in a sport, game, or battle
	come together
	come upon, as if by accident; meet with
	be beset by
	experience as a reaction