from the figure it appears that snAPI does not calculate the time differences between all photons, but rather focuses solely on those occurring in channel 2 immediately following channel 1, similar to the representation shown in the upper plot.
However snAPI indeed does calculate the time differences between all photons.
The figure in (https://picoquant.github.io/snAPI/snAPI.Main.html#snAPI_Main_Correlation)
from the figure it appears that snAPI does not calculate the time differences between all photons, but rather focuses solely on those occurring in channel 2 immediately following channel 1, similar to the representation shown in the upper plot.
However snAPI indeed does calculate the time differences between all photons.