There are actually TWO "calibration" temperatures for everything that measures relative density.
First you have the calibration temperature everyone knows about: The temperature at which you need to measure your sample. For most devices for the hobby this is 25°C/77°F or 20°C/68°F.
But now you have to think about what your device is measuring relative to. Fresh water at 25°C/77°F? Fresh water at 20°C/68°F? Fresh water at 4°C/39.2°F where water reaches its densest point?
This actually depends on the device and the standard the manufacturer chose. In theory the manufacturer could make the device yield measurements relative to 100% Ethanol at a certain temperature instead of fresh water (not really happening for devices designed for this hobby but you get the idea).
For example: I have a Hydrometer that measures a sample at 25°C/77°F relative to the manufacturer's standard solution which is fresh water at 4°C. On the hydrometer is a small text saying Sp.Gr. 25/4 to point this out. I also have a refractometer which measures a sample at 20°C/68°F relative to a different manufacturer's standard which is fresh water at 20°C/68°F. If you look through your refractometer you might see a text d20/20 or d68/68 which points this out.
What does this mean for my measurements?
Fresh water is denser at 4°C/39.2°F than at 20°C/68°F. So if I get a reading of for example 1.025 on my hydrometer this would be around 37ppt. But on my Refractometer 1.025 would mean around 35.5ppt. Not an enormous difference, but it can still cause confusion why to devices show different values even though the same sample is measured and the instructions were followed carefully (measured at the devices calibration temperatures so no adjustment is necessary).
I hope this was understandable. Most people seem unaware of this issue as the differences are small and the measuring devices used for the hobby aren't necessarily that precise. But I've read so many people claiming they don't use device X because it showed different values than their newly bought Refractometer/hydrometer/tds meter. Most of them work absolutely fine, but you need to understand that 1.023 on device A might mean something different than on device B and that it has nothing to do with the temperature at which you have to take the measurement.
Thanks.
I am aware of the variety of issues and complications around measurement and comparison temps for hydrometers and have a detailed article on it. It’s not so much of an issue for refractometers or conductivity meters as those generally correct themselves electronically or mechanically.
https://reefs.com/magazine/chemistry-and-the-aquarium-specific-gravity-oh-how-complicated/
But specific gravity (as opposed to a hydrometer reading) is typically defined as the density of the fluid divided by the density of pure water at the same temp, and it does not change very much with temperature unless one makes big temp changes.
It was your mention of different devices that was throwing me. I’d be wary of using the sort of ppt conversion tables you mention for unusual hydrometers (say, the 25/4 you mention) since the conversion may not be generated for seawater.