face vs countenance

face and countenance both are nouns.

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

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

Other hypernyms of face include visage.

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

face: the front of the human head from the forehead to the chin and ear to ear
countenance: the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)

Other hyponyms of face include kisser, mug, phiz, physiognomy, smiler, visage.

face (noun)	countenance (noun)
a vertical surface of a building or cliff	the appearance conveyed by a person's face
the side upon which the use of a thing depends (usually the most prominent surface of an object)	the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)
the striking or working surface of an implement	formal and explicit approval
the general outward appearance of something
status in the eyes of others
impudent aggressiveness
the feelings expressed on a person's face
the front of the human head from the forehead to the chin and ear to ear
the part of an animal corresponding to the human face
a specific size and style of type within a type family
a contorted facial expression
a surface forming part of the outside of an object
a part of a person that is used to refer to a person

face (verb)	countenance (verb)
deal with (something unpleasant) head on	consent to, give permission; permit
present somebody with something, usually to accuse or criticize
oppose, as in hostility or a competition
line the edge (of a garment) with a different material
cover the front or surface of
turn so as to face; turn the face in a certain direction
turn so as to expose the face
be oriented in a certain direction, often with respect to another reference point; be opposite to
be opposite