Sidereal and tropical used as terms for two systems of ecliptic coordinates used in astrology.
Both divide the ecliptic into a number of "signs" named after constellations, but while the sidereal system defines the signs based on the fixed stars, the tropical system defines it based on the position of vernal equinox (i.e. the intersection of the ecliptic with the celestial equator). Because of the precession of the equinoxes, the two systems do not remain fixed relative to each other but drift apart by about 1.4 arc degrees per century.
The tropical system was adopted during the Hellenistic period and remains prevalent in western astrology. A sidereal system is used in Hindu astrology, and in some 20th-century systems of western astrology.
While classical tropical astrology is based on the orientation of the Earth relative to the Sun and planets of the solar system, sidereal astrology deals with the position of the Earth relative to both of these as well as the stars of the celestial sphere. The actual positions of certain fixed stars as well as their constellations is an additional consideration in the horoscope.
The classical zodiac was introduced in the neo-Babylonian period (ca. 7th to 6th century BC). At the time, the precession of the equinoxes had not been discovered. Classical Hellenistic astrology consequently developed without consideration of the effects of precession. The discovery of the precession of the equinoxes is attributed to Hipparchus, a Greek astronomer active in the later Hellenistic period (ca. 130 BCE).
Ptolemy writing some 250 years after Hipparchus was thus aware of the effects of precession. He opted for a definition of the zodiac based on the point of vernal equinox, i.e. the tropical system. While Ptolemy noted that Ophiuchus is in contact with the ecliptic, he was aware that the twelve signs were just conventional names for 30 degrees segments (especially since the Aries sign had ceased to be in contact with the Aries constellation already in his time).
The Hindu Jyotisha system opted for defining the zodiac based on the fixed stars, i.e. directly tied to the eponymous zodiacal constellations unlike Western astrological systems.
Traditional Hindu astrology is based on the sidereal or visible zodiac, accounting for the shift of the equinoxes by a correction called ayanamsa. The difference between the Vedic and the Western zodiacs is currently around 24 degrees. This corresponds to a separation of c. 1700 years, when the vernal equinox was approximately at the center of the constellation Pisces and the tropical zodiac coincided with the sidereal one (around 290 AD, or at 23.86° as of 2000 according to N. C. Lahiri, renowned author of Lahiri's Ephemeris published from kolkata, India. The separation is believed to have taken place in the centuries following Ptolemy (2nd century AD), apparently going back to Indo-Greek transmission of the system. But earlier Greek astronomers like Eudoxus spoke of vernal equinox at 15° in Aries, while later Greeks spoke of vernal equinox at 8° and then 0° in Aries (cf. p. 16, S. Jim Tester in ref.), which suggests use of sidereal zodiac in Greece before Ptolemy and Hipparchus.
Some western astrologists have shown interest in the sidereal system during the 20th century.
Cyril Fagan assumes the origin of the zodiac in 786 BC, when the vernal equinox lay somewhere in mid-Aries, based on a major conjunction that occurred that year, corresponding to a difference of some 39 degrees or days.
Most sidereal astrologers simply divide the ecliptic into 12 equal signs of 30 degrees but approximately aligned to the 12 zodiac constellations. Assuming an origin of the system in 786 BCE, this results in an identical system as that of the classical tropical zodiac, shifted by 25.5 days, i.e., if in tropical astrology, Aries is taken to begin at March 21, sidereal Aries will begin on April 15.
But a small number of sidereal astrologers do not take the astrological signs as an equal division of the ecliptic, but define their signs based on the actual width of the individual constellations. Stephen Schmidt in 1970 introduced Astrology 14, a system with additional signs based on the constellations of Ophiuchus and Cetus.