encounter vs run across

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

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

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

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

encounter (noun)	run across (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

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