encounter vs run into

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

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

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

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

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

encounter (noun)	run into (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 into (verb)
contend against an opponent in a sport, game, or battle	collide violently with an obstacle
come together	hit against; come into sudden contact with
come upon, as if by accident; meet with	come together
be beset by	be beset by
experience as a reaction