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I had speculated that the definition of the "stellar day" might have originated from some random Wikipedia editor. In this case, Dave Walden found a reference which indicates that it probably originated from a legitimate source (probably!). That reference: https://hpiers.obspm.fr/eop-pc/models/constants_mobile.html defines the "stellar day" as "... referred to the stars is not affected by the precession and therefore is slightly larger than the sidereal day". That's a good start, but who invented this poor terminology? Need an alternative name? How about the "inertial day" or even the "true day" since the day that's being described here is the true rotation period relative to the best modern definition of non-rotation in the cosmological sense. "Stellar day" remains much too close to "sidereal day" linguistically.

You might wonder: why not just call the "true day" the "sidereal day", which is how it has been generally understood for a very long time? The excuse here (a reasonable excuse) is that this definition falls in line with the definition of sidereal time: the local sidereal time is the RA (right ascension) of the observer's zenith. Sidereal time has to be tied to the equatorial coordinate grid to make his happen, and that shifts slowly thanks to precession. The "sidereal day" defined to align with this definition of "sidereal time" is not quite the true rotation period of the Earth.

Frank Reed