I might be wrong, but for OG calculations, I think the only thing that Sean’s does that others may not is to use a wort correction factor. Just for sanity-check, you can set the wort correction factor to 1.00 and it will probably give you the same answer as other calculators.
This is only for sanity-checking, though, because for calculations that need to be accurate, wort correction is a must.
Now, on FG and any other calcs after fermentation has started, the differences are much greater and more complex…
The wort correction factor, usually 1.04, is used to adjust the reading for wort versus the sugar-water solution that the refractometer is designed to measure, so don’t mess with that. Sean’s calculator is based on real-world results with post-pitch beer and he made a new model that is pretty darn accurate over a range of readings - I trust it more than any of the calculators using the “standard” formula.
Sean’s spreadsheet is highly reliable for beers that are not ultra huge or which are finishing ultra low, according to his statements. Highly accurate for most beers!
If you’re talking about pre-fermentation OG reading, the calculators say different things because they are using a different polynomial to curve-fit the brix to SG tables. The ‘official’ polynomial is the ASBC polynomial, what promash uses, which AJDelange posted on the BN forums a couple years ago:
Putting this into the excel solver says 1.07765 for 18.8°P. The refractometer correction factor is applied to this, so divide the right side of the decimal by your correction factor (1.02-1.04) to get the actual wort S.G., which should be most comparable to the hydrometer.