The Backlights for LCD displays are white LEDs, which are made by using a Blue LED together with a yellow phosphor to transform some of the light for the Red and Green primaries. The spectrum of an LCD display is just the spectrum of its white LED Backlight filtered through the individual Red, Green and Blue sub-pixel filters within the LCD panel, resulting in broad rolling spectra for LCDs.
OLEDs are emissive devices so their spectra are just the sum of the individual Red, Green and Blue OLED spectra, modified slightly by the touchscreen layer and anti-reflection absorption layer through which their light must pass.
As expected the Galaxy Note 3 OLED spectra are relatively narrow with deep notches between the primaries, which results in highly saturated colors that are adjusted with display Color Management to improve image color accuracy.
The difference in the relative heights of the Green and Red Primary peaks for the Adapt Display and Movie modes is due to their different White Points, which requires different drive levels for each primary.