True sidereal astrology, sometimes referred to as 'constellational', or 'astronomical' astrology, is a branch of western astrology practiced using the actual stars instead of a simplified or approximate zodiac. "Sidereal" means "oriented to the stars". In true sidereal astrology, the size of the signs is not uniform... it matches with the sizes of the constellations which give them their names. This stands in contrast to most forms of western astrology, which use a zodiac of 12 signs of uniform size (mostly for simplicity's sake). Mainstream western astrology (aka "tropical astrology") is based on a zodiac which is not even oriented to the stars. It can be quite confusing, but it can also be worth understanding! Let's look a little closer...
Did you know that mainstream western astrology came from our ancestral star-watching roots? ...that the western zodiac signs (Aries, Taurus, Gemini, etc) are named after the constellations that the planets and luminaries pass through? Ok... did you know that in ancient times and through its development, astrology was aligned precisely with the science of astronomy, but was de-coupled from science almost 2000 years ago, when most people thought that the Earth was the absolute center of a universe which rotated around it? Astrology in the west hasn't lined up with the actual sky since then, even though all of the classic (Ptolemaic) ideas about zodiac signs that we have today arose from scientific sky-watching! The story gets worse...
Once known as "divination by means of astronomy" in ancient Greece, astrology today drifts ever-further out of alignment with the actual heavens. This is due largely to the slow drift of the stars (relative to our seasons), or 'precession of the equinox'. The stars seem to drift at a rate of 1° every 72 years, barely enough to notice but if you chart the position of sunrise at the equinoxes, you would see this change. Over centuries, the mainstream western zodiac has shifted ~25° out of alignment with the constellations of the living sky. Since a standard zodiac sign is only 30°, western mainstream astrology today is out of tune by almost a whole sign!
Unlike any other system of astrology ever practiced, mainstream western astrology (aka "tropical astrology") orients its zodiac to the seasons of the northern hemisphere instead of the stars. This view is not only geo-centric (Earth-centered), but also Euro-centric (the seasons are opposite in the southern hemisphere!)... while today we know that our solar system is helio-centric (Sun-centered). We also know that the fixed stars drift over time relative to the Earth's orientation and the seasons... but our mainstream western zodiac remains oriented to an idea which reflects the fundamental ignorance of a bygone era. In ancient Greece, Aristotle and other popular thinkers promoted the idea that the entire cosmos revolved around an unmoving Earth at its center. The tropical zodiac and what would become modern mainstream astrology arose in the shadow of that error.
Although the astronomer & astrologer Claudius Ptolemy, in the 2nd century AD, noted that the star positions had changed slightly over the centuries, he did not have the foundation of knowledge needed to understand why this was so. He seems to have thought that the fixed stars were moving, and therefore untrustworthy... hence he adopted the idea that the zodiac should be organized around the spring equinox sunrise, which seemed to him much more trustworthy (since of course the Earth was fixed, but the cosmos obviously moved!) Ptolemy's works on astronomy and astrology are some of the only surviving works on those subjects from his time period, and he is generally credited with being the main reason that Greek astrology shifted its orientation to the tropical zodiac. Each year, the tropical zodiac is adjusted so that 0° Aries aligns with the sunrise of the spring equinox (regardless of what constellation the Sun is actually rising in), so another name for the tropical zodiac is the "moving zodiac".
The spring equinox sun hasn't actually risen at 0° of constellation Aries since Claudius Ptolemy was alive, (it's currently well into Pisces and around 2770 will enter Aquarius) and of course in the 2nd century, there was no meaningful difference between tropical and sidereal zodiacs! Over time, a sidereal zodiac will always be aligned to the stars and constellations as they are in the living sky... but over that same amount of time, a tropical zodiac will slowly fall out of alignment with the heavens, like a clock that's only right once every ~22,000 years... so what do we do until then?
In a lifetime, we don't really notice much difference in the stars, but over the course of centuries and millennia, major differences develop (see image above of the tropical zodiac compared to the living stars: Note that sign Libra is populated by constellation Virgo, sign Virgo by constellation Leo, and so on.). The practice of true sidereal astrology organizes itself around the actual skies, and remains accurate to them. If the Moon is in the stars of constellation Virgo, true sidereal astrology says it's in Virgo. We don't say that it's 'in Libra'. This is the way that astrology was practiced by our ancient ancestors worldwide. Sky-watchers such as the ancient Greeks, Egyptians, Mayans, Sumerians, Babylonians, Tibetans, Chinese, and Indian cultures all charted the activities of the planets and luminaries through the actual stars, comparing these with patterns of activity on earth and within people's psyches... and this is where the discipline of astrology comes from.
True sidereal astrology, through the Greek tradition, arose historically from Babylonian celestial science. In ancient Babylon they used 18 unevenly sized constellations, which were later simplified to the 12 even zodiacal signs we know today. This simplification allowed astrology to survive the European dark ages, during which people were not widely numerate. Today we have the computing technology to return to the ancient roots of astrological practice, and calculations which would have taken months and been reserved strictly for royalty now take just minutes, and are available to you!