1 Mean Solar Day = 24:03:56.55536 of mean siderial time,
1 Mean Solar Day = 1.00273791 earth rotations with respect to the Mean Vernal Equinox,
1 Mean Solar Day = 1.0027378118868 earth rotations with respect to the Mean position of Stars,
1 Mean Solar Day = 1 earth rotation with respect to the Mean Sun position - EXACTLY!
I like the last one best.
1 mean siderial day = 23:56:04.09054 of mean solar time.
Tim Zukas nailed it, the very small difference (approximately 4 minutes) between the apparent solar day and the siderial day is that the earth moves along it's orbit of the sun by about the equivalent of 4 minutes by the time the sun returns to the same Longitude. The very small variation in the actual solar day (which is why we have to refer to the MEAN day) that Tim alludes to is because the earth's speed around the sun varies slightly because it follows an ellipse, not a perfect circular orbit.
Regards,
Old Smokey