smirk vs grinning

smirk and grinning both are nouns.

Word	Noun	Adjective	Verb	Adverb
smirk	Yes	No	Yes	No
grinning	Yes	No	No	No

As nouns, grinning is a hypernym of smirk; that is, grinning is a word with a broader meaning than smirk:

smirk: a smile expressing smugness or scorn instead of pleasure
grinning: a facial expression characterized by turning up the corners of the mouth; usually shows pleasure or amusement

Other hypernyms of smirk include grin, smile, smiling.

smirk (noun)	grinning (noun)
a smile expressing smugness or scorn instead of pleasure	a facial expression characterized by turning up the corners of the mouth; usually shows pleasure or amusement

smirk (verb)	grinning (verb)
smile affectedly or derisively