Additional to the modes already available in the desktop background setting dialogue, most other desktop enviroments have also another mode, mostly called zoom.
This mode fills the whole screen with the background image, but without stretching it unnatural.
It is done by scale the image on the shorter side of the image till it reaches the end of the screen, but proportionally. The longer side will be scaled outside the screen, equally both on both sides. (Centered)
This is the preferred way when using a background image who is not in the native resolution and also not in the same screen ratio as the own monitor.
Stretching and tiling is mostly unused and far less important than a "zooming" function.
(I hope you understand my english)