glower vs make a face

glower is a noun but make a face is not a noun.

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

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

glower: look angry or sullen, wrinkle one's forehead, as if to signal disapproval
make a face: contort the face to indicate a certain mental or emotional state

Other hypernyms of glower include grimace, pull a face.

glower (noun)	make a face (noun)
an angry stare

glower (verb)	make a face (verb)
look angry or sullen, wrinkle one's forehead, as if to signal disapproval	contort the face to indicate a certain mental or emotional state
look at with a fixed gaze