"They aren't the same," our mentor explained. "In a Shooting only one person fires a gun and the average round count is one to three shots. However, a Gunfight involves multiple parties all firing guns and the average number of shots fired is whatever happens to be in the gun."
I think that is a rather cut and dry definition on scenarios that are not at all cut and dry.
I still believe that since the criminal initiated the conflict by producing a weapon and leaving the guard with only one option, to fire in defense, would qualify it as a gunfight, even though the criminal did not have the guts to stay and fight back, but YMMV.
Due to media usage of the term "shooting", it does leave a rather sour taste in my mouth to use it in this situation. Just ask yourself, who initiated this "shooting"? IMO, if it was the security guard, then yes it was a shooting. If it was the criminal, then I say that it was a gunfight because the security guard had no choice but to match deadly force with equal force (gun vs. gun).