Hello Kaiwen,
What is printed in the output file is the restricted stopping power (following the 2nd expression you point above).
Using DEFAULTS with HADROTHE, the delta-ray production threshold is 300 keV.
Using DEFAULTS with PRECISIOn, the delta-ray production threshold is 100 keV, i.e. more of the ionization losses are sampled explicitly as delta rays instead of in an aggregate manner along the step via a stopping power, hence the PRECISIO stopping power is lower than that with HADROTHE in your plot.
You may also want to take a look at this post.
Hope this helps,
Cesc