Hi Emma,
I glad that you found the source of the discrepancy!
The difference between discrete and histogram is that for the second one you will sample
particles with energies within bin width and not discrete lines. It’s more realistic for sources with continuous spectra.
In my example, I have used histogram definition for both FLUKA and PHITS.
Please always check that source types, scoring and especially normalization are consistent between both codes. Your Phits histogram definition was shifted by one bin to the right in comparison with Fluka.
Here is an example how it should be defined in Phits:
Here is comparison for your spectra with histogram definition for small statistics .
As you see, it is also in relative agreement with discrete definition.
Best wishes,
Volodymyr