poker face vs countenance

poker face and countenance both are nouns.

Word	Noun	Adjective	Verb	Adverb
poker face	Yes	No	No	No
countenance	Yes	No	Yes	No

As nouns, countenance is a hypernym of poker face; that is, countenance is a word with a broader meaning than poker face:

poker face: a face without any interpretable expression (as that of a good poker player)
countenance: the appearance conveyed by a person's face

Other hypernyms of poker face include visage.

poker face (noun)	countenance (noun)
a face without any interpretable expression (as that of a good poker player)	the appearance conveyed by a person's face
	the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)
	formal and explicit approval

poker face (verb)	countenance (verb)
	consent to, give permission; permit