calculation of elapsed time by the apparent position of the sun
On a prograde planet like the Earth, the sidereal day is shorter than the solar day. At time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again (1→2 = one sidereal day). But it is not until a little later, at time 3, that the Sun is overhead again (1→3 = one solar day). Or more simply, 1-2 is a complete rotation of the Earth. However because the Earth moving around the Sun affects the angle the Sun hits a position on the Earth, 1-3 is how long it takes noon to happen again.
A solar day is a unit of time. It is a cycle of day and night.