DOSE-H2O corresponds (as the name says) to dose-to-water, calculated by weighting the tracklength with the stopping power in water at every step (no matter if the material at the step location is different).
While DOSE is calculated as the real energy deposition per mass.
DOSE-H2O is typically used in the medical environment to compare with the output of TPS systems as well for the calculation of the RBE
Please look the post
especially the appendix of the quoted paper.