grin vs facial gesture

grin and facial gesture both are nouns.

Word	Noun	Adjective	Verb	Adverb
grin	Yes	No	Yes	No
facial gesture	Yes	No	No	No

As nouns, facial gesture is a hypernym of grin; that is, facial gesture is a word with a broader meaning than grin:

grin: a facial expression characterized by turning up the corners of the mouth; usually shows pleasure or amusement
facial gesture: a gesture executed with the facial muscles

Other hypernyms of grin include facial expression.

grin (noun)	facial gesture (noun)
a facial expression characterized by turning up the corners of the mouth; usually shows pleasure or amusement	a gesture executed with the facial muscles

grin (verb)	facial gesture (verb)
to draw back the lips and reveal the teeth, in a smile, grimace, or snarl