Using a hitscan weapon the direction is the vector that you are referring to, but for a projectile it is the normalized velocity.
With a hitscan fire type the direction will be in the direction of the hitscan raycast. You could draw a debug line to see that by outputting the fireDirection within ShootableWeapon.HitscanFire.
Third person mode is a bit different because the ray isn't being fired directly in the center of the camera. The weapon is always going to be fired towards the crosshairs, and with the third person camera offset that direction will have a slight offset in order to compensate for this.
Putting this here so that it possibly helps someone else....
I found a inspector variable that is probably designed to aim down the weapon. It is the "fire in look source direction" inspector variable. If you draw a debug ray, it will move exactly through the length of the weapon. The only other thing I needed to do is alter the x and y rotation of the weapon (in character structure) so that it lines up with the impact position on the target.
Tested with shotgun and pistol, so far so good.