The power spectral density of white noise is independent of frequency. There is the same amount of energy within any two different but identically sized frequency intervals. E.g. 84-86Hz and 543-545Hz. A narrow band FFT analysis of white noise will show as flat. However octave band analysis will show the level to rise by 3dB per octave because each band has twice the frequency range of the preceding octave.
Pink noise is produced by filtering white noise to have the same power within each octave. Narrow band analysis will show a fall in level with increasing frequency, but third-octave band or octave band analysis results will be “flat”.