Precession refers to the astronomical fact that the point where the ecliptic crosses the celestial equator, which defines 0 degrees Aries in the tropical Zodiac, moves backwards along the equator about 50.2" (ie minutes of arc, or 50.2/60ths of 1/60th of 1/360th of the circle) per year. This is called the precession of the equinox.
A solar return is the return of the Sun to its position in the birth chart of the native.
But because the tropical Zodiac is moving backwards (ie precessing) , the Solar return Sun's natal position in the tropical Zodiac is different from its actual position in space at the time of birth (its sidereal position; it's position against the fixed stars, sideris). This difference increases every year, by 50.2".
This leaves us three alternatives.
1. Ignore the difference between the tropical and sidereal positions, and use the Sun's tropical birth position and tropical Zodiac. This is what most astrologers in the West currently do.
2. Calculate the return based on its sidereal position and use the Sidereal Zodiac. This is what advocates of the Western Siderealist school (Fagan, Firebrace, Bradley/Allen, et al) do.
3. Calculate the return based on the Sun's sidereal position, but present the chart in terms of the tropical Zodiac. This is what is properly referred to as a precessed Solar return. There are a number of ways to present this, which can create some confusion, but that's basically it.
Options 2 and 3 will both be calculated for the same time, and the planets will be in the same houses, but the signs will be different, since they present different Zodiacs (the Sidereal for 2 and the tropical for 3). Option 1 will be for an earlier time, and the planets will be in different houses, and the Moon and faster planets will be in slightly different positions, depending on the age of the native. The angles of the chart will also be different.
By the time the native is 72 or so, the two returns will be more or less a day apart, so at age 36, more or less 12 hours apart, etc.
All three options have their advocates. I've personally used options 1 and 3, and currently favor 1. But as I say, all have their advocates.