I want to change the login background on Elementary, but ONLY that one
It's quite simple, but not as intuitive unfortunately.
All images used as wallpaper from /usr/share/backgrounds will be applied by LOKI to both Desktop and Login (permissions matter too!)
To keep them separate, use an image from /usr/share/backgrounds as your login BG with greeter config line (must be unhashed!) at /etc/lightdm/pantheon-greeter.conf:
And to set different wall for the destop only, choose an image from any other location in the system, and use right clik->set as wallpaper - that should keep them separate. Tested it on LOKI and JUNO Beta2 and it works.
Setting desktop wallpaper this way copies your chosen image to /home/YOURUSER/.local/share/backgrounds/ and imports it to Settings->Desktop->Wallpaper. This unfortunate way, its up to you to remember which image is from here...
/usr/share/backgrounds (applies to both Desktop and Login)
/home/YOURUSER/.local/share/backgrounds/ (applies to Desktop only)