smiling vs smirk

smiling and smirk both are nouns.

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

As nouns, smirk is a hyponym of smiling; that is, smirk is a word with a more specific, narrower meaning than smiling:

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

Other hyponyms of smiling include simper.

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

smiling (adjective)	smirk (adjective)
smiling with happiness or optimism

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