As previously discussed, the Moon moves to the east among the stars once every 27.3 days, along a path which is tilted by about 23 1/2 degrees, on the average, relative to the Celestial Equator. It also moves relative to the Sun once to the east every 29.5 days, because its eastward motion (about 13 degrees per day) is much faster than the Sun's eastward motion (about 1 degree per day). This relative motion changes the portion of the Moon which we see lit, but does not change the portion turned toward us, which is always the same (compare the seas shown in the crescent and new moon photos below).
A brief examination of the images below might give the impression that they are identical, because the crescents have the same shape, the portion of the Moon lit by earthlight looks about the same (the same side always being turned toward us), and the Moon is in the same place, just to the east of the Pleiades, a star cluster in Taurus. But they are not at all the same, as discussed in the caption between them. (Much, much more to follow)
Above (Vincent Jacques, apod060629) and below (Jerry Lodriguss, apod050414), two views of the Moon and the Pleiades. What is the difference between these two photos? In each case, the Moon is on the eastern side of the Pleiades and is a relatively thin crescent; but in the first image the Moon is lit on the right, and in the second image it is lit on the left. This difference means that the earlier image (below) was taken in the evening, when the Moon was a waxing crescent, east of the Sun in the sky and "growing" each night as its elongation (distance from the Sun) increased. The later image (above) was taken before dawn, when the Moon was a waning crescent, west of the Sun in the sky and "shrinking" each night as its elongation decreased. (Note: Since the Moon was rising in one case and setting in the other case, the top image had to be rotated 90 degrees to make them appear so similar. If the waning crescent Moon had really been lit on the upper left, the Sun would have been up and to the left of it, which means it would have been daylight, and the Pleiades would not have been visible.)