An improvisation is a spontaneous dialogue between any number of players or actors. If the premise and facts of the improvisation are fictional (improv comedy or Jamie Kennedy's pranks, which some view as somedy) than the "improv" is fictional.Psycologists use a technique called Role Playing in which the participants improvise scenes that are fictional (because they are "acting" them in the shrink's office) but with premises based on facts from the actual participants' lives. Still "fictional" because they are being acted out in a controlled context, even if the actors and "facts" are real.
When some guy gets a ticket and starts engaging the cop in a "I looked at my speedometer and I wasn't going over 35, I KNOW it!" that's a bit of "real" improvisation.
If Matt is an actor then the director's reactions to his actions are "fake." If Matt is actually being fooled then the reactions are "real."
I think it was best said by the German philosopher Werner Heisinger - inventor of the Nobel Prize winning "Uncertainty Principle," who remarked: "Why do you all waste so much valuable time worrying about this crap!"