Diurnal motion does not affect all celestial objects equally, but the difference is so small that you can usually ignore it. Because the Earth orbits the Sun, the
stars seem to gain four minutes per day relative to solar time; that is, a sidereal day, measured between successive meridian passages of the same star, is only 23 hours and 56 minutes.
Accordingly, telescope drives offer a choice between solar rate (one rotation per 24 hours) and sidereal rate, which is about 2.7% faster.
The difference between sidereal and solar rate is hardly noticeable. If you track the stars at the solar rate, the total tracking error will be about one degree per day, or 0.1° in two and a half hours.
Celestron telescopes also offer King rate, defined by E. S. King at Harvard in 1931, which is slightly faster than sidereal rate in order to compensate for atmospheric refraction.
Lunar rate is more problematic. The Moon's orbital motion is fast enough to make sidereal and solar rates unsuitable; if you track the Moon at the sidereal or solar rate, it will move completely out of the telescope field in an hour or so. Ignoring parallax, lunar rate should be 3.3% slower than solar rate, and that is what most telescope drives deliver. But the apparent motion of the Moon also depends on parallax; you are significantly closer to the Moon when it is high in the sky than when it is rising or setting. Further, the Moon is moving in declination as well as right ascension. The result is that no single lunar rate is correct all of the time.
It would be straightforward to have the computer automatically select lunar rate when you are observing the Moon, solar rate for the Sun and planets, and sidereal rate for everything else. I am not aware of a computerized telescope that actually does this.
Having said all this, let me point out that the tracking rates of some of the less expensive computerized telescopes are not particularly accurate; the object may wander all over the field of a high-power eyepiece. Telescopes with servo motors and worm drives (such as the Meade LX200) are more precise.
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