Re: Assault vs Defense of Property
I suspect you might be referring to a situation that is often called brandishing a firearm. That is where a person, even if not actually pointing the weapon or even holding it presents it in such a manner as to specifically make it known they are carrying a firearm. As an example, if a person were to confront the trespasser while carrying a weapon hidden by a coat or shirt and makes the effort to expose it would be considered brandishing the firearm. Since there is an implied threat, in some cases, that could be considered an assault.
I have not researched this in terms of Arizona law though. Refer to the links Mr. K has provided for specific applications.
I am not an attorney and any advice is not to be construed as legal advice. You might even want to ignore my advice. Actually, there are plenty of real attorneys that you might want to ignore as well.