bullseye
Campaign Veteran
It is not a legal difference, meaning the words are legally defined seperately. What I refer to is the perception of the judge/jury when they hear those two terms being used.
The NRA is very zealous in removing the use of the word "weapon" from your vocabulary during their instructor training courses. "Weapon" has the connotation of being offensive in nature. Weapons also encompass more than just firearms; think Weapons of Mass Destruction (WMDs), Nuclear Weapons, etc. Many (sheeple) who hear the word "weapon", associate it with death, often lots of it! An anti would never dream of using "select-fire firearm" in place of "assault weapon"! The use of the words firearm, handgun, rifle, and shotgun aren't perceived with the same aggressive tone as weapon. We go to war with weapons, but use firearms for a wide array of activities: self-defense, hunting, sporting purposes, etc.
Those who have served in the military have the word ingrained in the psyche, most can probably recall the unfortunate servicemember who referred to their rifle as a "gun" instead of rifle or weapon. The ensuing on-the-spot correction has the servicemember holding the rifle in the air with one hand, grabbing the crotch with the other, and singing something like "This is my weapon, this is my gun - this is for killin', this is for fun."
There are differences in the legal definitions:
Weapon: http://definitions.uslegal.com/w/weapon/
Firearm: http://definitions.uslegal.com/f/firearms/