smile vs pull a face

smile is a noun but pull a face is not a noun.

Word	Noun	Adjective	Verb	Adverb
smile	Yes	No	Yes	No
pull a face	No	No	Yes	No

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

smile: change one's facial expression by spreading the lips, often to signal pleasure
pull a face: contort the face to indicate a certain mental or emotional state

Other hypernyms of smile include grimace, make a face.

smile (noun)	pull a face (noun)
a facial expression characterized by turning up the corners of the mouth; usually shows pleasure or amusement

smile (verb)	pull a face (verb)
change one's facial expression by spreading the lips, often to signal pleasure	contort the face to indicate a certain mental or emotional state
express with a smile