The Ambiguity of Acting

Got a good one from my logic class yesterday. The word "act" is ambiguous, even as a verb. One can act on a stage -- that is represent a character distinct from the actor -- and one can simply do what one does, as in "act your age." Take the first meaning, the dramatic sense of act in which one portrays someone else. Now, if we consider a situation in which one presents a face different from what one's natural inclination would be, say, if you try to hide your fear while giving a class presentation or if you gratefully thank someone for a gift you really dislike, is that sense of acting brave and acting thankful the same or a different sense of the word "act" from what someone does on the stage?