Any background image that you use is a fixed pixel size. Whether the monitor is 15'' or 19'' isn't as important as understanding the resolution used. A 600 pixel wide image is always 600 pixels wide, but may look relatively larger or smaller, in inches and area of the screen, depending on the resolution.
Most of the time, if someone has a graphical background, they are using a small (in pixels) size graphic that can be tiled to fill the screen. Tiling works at any resolution, although the size of the tile relative to the resolution will change the way the tiling appears. In other words, a 3x3 tile will look big at 640x480 resolution, but small at 1280x768.
Probably more than you want to know, but hopefully it makes sense and is useful.