make a face vs pout

make a face is not a noun while pout is a noun.

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

As verbs, pout is a hyponym of make a face; that is, pout is a word with a more specific, narrower meaning than make a face:

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

Other hyponyms of make a face include squinch, squint, wince, smile, frown, glower, lour, lower, screw up, mop, mow.

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

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