In lang=en terms the difference between countenance and conduct
is that
countenance is to tolerate, support, sanction, patronise or approve of something while
conduct is to carry out (something organized).
As nouns the difference between countenance and conduct
is that
countenance is appearance, especially the features and expression of the face while
conduct is the act or method of controlling or directing.
As verbs the difference between countenance and conduct
is that
countenance is to tolerate, support, sanction, patronise or approve of something while
conduct is (archaic|transitive) to lead, or guide; to escort.