I'm having trouble understanding precisely what a stellar day is. Neither the USNO nor the IERS sites provide a definition. And Wikipedia's description as the "rotation period relative to the fixed stars" as "the span of time it takes for the Earth to make one entire rotation with respect to the celestial background or a distant star" is confusing, since, relative to fixed stars, the earth is both rotating and precessing, so that the rotation period relative to fixed stars as such, is not a single value, but will be different for stars with different equatorial coordinates.
I assume that the stellar day is simply the earth's rotation period on its axis, but I'm not sure that's right, or how to state it formally (e.g. with respect to inertial frames).
I understand why the stellar day is distinct from and longer than the sidereal day, since the coordinate system that defines a sidereal day is rotating slowly against the rotation of the earth.