According to the Wikipedia article you reference, "stellar day" is supposedly a new name for a planet's sidereal rotation period. However, I cannot find any documentation of this new name anywhere, and that includes my copy of Explanatory Supplement to the Astronomical Almanac, 3rd edition, edited by Urban and Seidelmann (University Science Books, 2012) which was just published within the month. This source is definitive and the term doesn't appear therein (okay at least not in the index). However, further digging found reference to it here
http://hpiers.obspm.fr/eop-pc/models/constants.html
but I've yet to find an actual statement of the change in terminology from "sidereal rotation period" to "stellar day" anywhere in the IERS conventions. Anywhere, the distinction is that the sidereal day is measured relative to the moving vernal equinox, which accounts for precession, whereas the sidereal rotation period (stellar day) is relative to the fixed inertial frame of background stars.
Why are Lunar Eclipse more common than Solar Eclipse?
They aren't. Lunar eclipses and solar eclipses occur with almost equal frequency.
From http://eclipse.gsfc.nasa.gov/eclipse.html and pages within, there were / will be 11898 solar eclipses of all types and 12064 lunar eclipses of all types in the five millennia between 2000 BCE to 3000 CE. Lunar eclipses outnumber solar eclipses by less than 3% if you count eclipses of all types.
Of those 12064 lunar eclipses, 4237 were partial penumbral eclipses, in which at any one time only part of the Moon was in the Earth's penumbral shadow, and during the entirety of the event, none of the Moon entered the Earth's umbral shadow. These are extremely subtle eclipses, and because of this some people say they don't count as eclipses. If one discounts these partial penumbral lunar eclipses, then solar eclipses outnumber lunar eclipses by over 50%.
That's not quite fair because partial solar eclipses are also extremely subtle events. If one also discounts those partial solar eclipses, then solar eclipses (total, annular, and hybrid) slightly outnumber lunar eclipses (total and partial), but only by a mere 0.2%.
Another way to look at this is that lunar eclipses and solar eclipses occur with almost equal frequency.
However, for any one person, the odds of seeing a solar eclipse are rather small while the odds of seeing a lunar eclipse are quite large. One has to be willing and financially able to galavant around the globe to see solar eclipses. The path of totality of a solar eclipse covers but a tiny, tiny fraction of the Earth's surface. In comparison, about half of the Earth gets to see a total lunar eclipse.
Best Answer
We need some reference background to plot the "movement" of the Sun. If we could see the stars during the day, and we were to go to a fixed point on the equator and mark the location of the Sun each day at noon on a star chart, this point would move in a circle through the stars once per year. The Sun rotates around the Earth more slowly than the stars do, so the number of solar rotations is one fewer than the number of sidereal rotations.
Imagine walking counterclockwise around a circular track, facing North the whole time. Suppose there's a light in the middle of the track. If you start out in the Eastern part of the track, the light will start out on your left. Once you get to the Northern part of the track, the light will be at your back. When you get to the Western part, it will be on your right. At the Southern part, it will be in front of you. So the light will appear to rotate around you counterclockwise.
So if the Earth didn't rotate at all, the Sun would appear to rise and set once over the course of the year. This one circuit due to the revolution around the Sun cancels out one of the 366 circuits due to the rotation of the Earth, leaving only 365 solar cycles.