I use my refractometer only during the brewing process, then switch to the hydrometer for OG and FG readings.
As a rule; use a hydrometer for my final OG reading after running the wort into the fermenter. Once the yeast has been pitched and mixed well, I draw a sample into a graduated cylinder intended for this use and drop in my hydrometer and note the initial reading.
Because I drew the sample post-pitch, it ferments at about the same rate as the wort in my fermenter (I keep them side by side in the fermentation fridge). This way; I can check the gravity any time I want without risking infection in the fermenter.
You may use a refractometer for checking gravity during fermentation but will likely get erroneous readings as, for reasons beyond my current experience, alcohol seems to affect the way light passes through the fermenting beer giving "fuzzy" readings which is why I rely primarily on my hydrometer for readings from OG to FG.
There is a small correction factor between the two instruments I use, I simply note this on my brew sheet and let it be what it is. The readings on the refractometer can be calibrated using distilled water so I tend to trust those readings, and make my corrections on the hydrometer.
In summary, I use the numbers on the refractometer to track the gravity during the brew, and I use the hydrometer to get the numbers I need for calculating my ABV.