I have never used a refractometer, just read an article in BYO about calibration. I say this with very limited knowledge.
For a refractometer to be accurate it needs to be calibrated using the color of the beer currently being measured. This may be for an accurate SG, but not being calibrated this way, may not affect finding a stable reading which would indicate FG. Using a conversion tool, the refractometer may indicate SG is stable at 1.016. Using a hydrometer the stable SG may actually be 1.011.
I won't mind if anyone says I'm totally wrong.
Unsolicited advice on using a hydrometer.
Never pick it up, from the horizontal, by that thin neck. Only hold it by the neck if movement is vertical.
Never shake Starsan foam off. Don't need the Starsan anyway because the hydrometer can't be read accurately inside a carboy or bucket, and you drink the sample not return it.
Never lay it down on a table or counter top. Both these surfaces always tilt towards the edge. Rolling hydrometers accelerate rapidly. Place it in a margarine container or plastic cup that won't tip.
Always have a spare because stuff still happens, especially with a cat around.
(I still have the hydrometer I purchased in 1987.)