Hello caleigh64,
Thank you for participating in the Apple Support Communities! We understand that you're wanting to set a Live Wallpaper on your iPhone XR but you don't see an option to. We'd be happy to help provide more information.
The iPhone XR does not support Live Wallpaper, however you can set a Live Photo as your wallpaper as your friend has done in the top screenshot that you provided:
Change the wallpaper on your iPhone - Apple Support
Specifically, take a look at these sections:
To choose a Live wallpaper or a Live Photo, you need an iPhone 6s or later.
iPhone XR and iPhone SE (1st and 2nd generation) don't support Live Wallpaper.
If your wallpaper is a Live Photo, you can turn on either the Live Photo effect or Perspective Zoom, but not both at the same time.
Take care.