Actually a different issue. With CRTs and plasma, burn-in would actually burn an image into the phosphors of the screen.

OLEDs will slowly burn out after continued use, usually starting with the blue LEDs, giving a similar appearance, but not exactly the same (for example, you can only see the image persistence when displaying an image).

LCDs don’t have either issue, but sometimes crystals can get stuck in a specific orientation, leading to (usually temporary) image retention. Gets worse in very cold weather. This is rare, though.