There's hardly any difference anymore between desktop pictures and wallpaper. Some time ago, PC software could only display bitmap format (.bmp) files as background images, while Mac software could display jpeg format (.jpg) files, which are much smaller, and faster to download. So, originally, desktop pictures were jpeg files for Mac, and wallpaper images were bitmap files for PC. Most desktop background images on the Internet are now jpeg, since they work with current software on both platforms and are much faster to download.
Whether they're called desktop pictures or wallpaper, there are still a couple of differences between background images intended for Mac versus PC. First, some sizes are intended specifically for Mac or PC - 832 x 624 for Mac, as an example. Pictures will look best if they match your screen resolution.
Another difference is the placement of copyright notices and logos. Since the Finder menu bar on a Mac is at the top of the screen, some publishers place their logos or other text at the top of the picture so they'll be covered by the menu bar. It's the other way around on a PC. But logo and copyright placement varies widely, so whether background images are called desktop pictures or wallpaper often says nothing about logos or copyright notices, if there are any.
There's also a difference in standard brightness between PC and Mac computers. Pictures may look darker on a PC than on a Mac, but we haven't noticed that images called wallpaper tend to be any lighter than images called desktop pictures. If your desktop background picture looks too dark or too bright, adjusting the brightness of your screen should fix it.