If you fix the vertical field of view (FOVY), then the FOVX will increase accordingly the aspect ratio. The calculation is FOVX = aspect * FOVY, which means that you will see more in a 16:9 screen than in a 4:3 screen.
Hi, what Steve told is correct, but also the game must enable this type of display configuration. Most games query the display for the available resolutions and the engine renders with this choice. It is already independent.