But they're not different distances! They're taken the same distance away. The wider angle means more of the environment is squeezed into the same amount of screen space so you see more, but everything's smaller.
This is an example from photography. http://www.nikonusa.com/en/Learn-And-Explore/Article/g3cu6o2o/understanding-focal-length.html
It shows the same image taken with different lenses. The photography world uses focal length though (with good reason as that's indepedent of aspect...), so a conversion to angular FOV in a 3:2 photograph is:
Now for any of those images, if the lens is kept the same but the film/sensor made wider, you'd record more of the detail in a wider picture. The focal length doesn't change, but the aspect would. If you were to take the 35mm lens and take a 16:9 photo with it, you'd get about the same detail horizontally as the 18mm photo. If you used a longer lens like the 85 mm, you'd need to shoot a panoramic shot to record all the buildings along the horizon in the 18 mm photo. However, you'd also lose all the top and bottom area.Code:Length : degrees horizontal FOV 18 : 90 24 : 74 35 : 54 55 : 36 85 : 23 105 : 20
So for a given focal length, yes, increasing horizontal size makes for a wider FOV, but focal length and 'sensor size' are completely selectable by the game. It's even used to effect, with wide-angle lenses with a wide FOV being used in games to simulate drunkeness and the like.
Camera settings in game include vertical size of the sensor. In the above photographs, we only see less of the sky and ground because the sensor is a 3:2 aspect. There literally isn't any film or CCD to record the info above and below what's recorded in the image. What we have in the Order is a horizontal FOV chosen by the camera setting, and a cinematic aspect chosen by the sensor or print setting. It's like printing a photo with a 55mm lens and then chopping off the top and bottom to make a super widescreen photo. It's the same horizontal FOV but reduced vertical FOV.
You're right, it should, but guns in FPS are typically drawn on top of the main game. That's why you can walk up to someone's face and have their face fill the screen and your massive assault rifle be only as big as their nose.
I see what you are talking about. But in terms of a game I fail to see the benefit. In your example the change in FOV is accompanied by a change of position and orientation in space of the gun.
If the gun size isn't changing, the aspect ratio hasn't changed or the game isn't distorting imagery to provide a wider or taller view, then the game is practically just moving the position of the player in space.
To mimic your bf3 example with a real camera, I would need gun on a stand. Everytime I changed the focal length I would have to reposition the gun stand to maintain a static size and position within each image. The camera may not be changing its position in space but the gun stand is and that is what helps a player orient his/her position in space not the camera.