pout vs pull a face

pout is a noun but pull a face is not a noun.

Word	Noun	Adjective	Verb	Adverb
pout	Yes	No	Yes	No
pull a face	No	No	Yes	No

As verbs, pull a face is a hypernym of pout; that is, pull a face is a word with a broader meaning than pout:

pout: make a sad face and thrust out one's lower lip
pull a face: contort the face to indicate a certain mental or emotional state

Other hypernyms of pout include grimace, make a face.

pout (noun)	pull a face (noun)
catfish common in eastern United States
marine eellike mostly bottom-dwelling fishes of northern seas
a disdainful grimace

pout (verb)	pull a face (verb)
make a sad face and thrust out one's lower lip	contort the face to indicate a certain mental or emotional state
be in a huff and display one's displeasure