Tropical Astrology is the old astrological division of the sky. When the Zodiac was invented, the position of the constellations were written down. But since then, the whole Zodiac has shifted almost a whole sign due to the Precession, so whoever was once born a Virgo, is now probably born a Leo - with the personality changes that come with it. Tropical Astrology ignores this, and keeps using the old tables - which have nothing to do with where the planets actually are in the sky.
Sidereal Astrology acknowledges the problem with the shifting signs, but digs itself deeper into the ludicrous: The more sidereal astrologers try to follow the real division of the sky, the more they are distancing themselves from the old wisdom. Sidereal astrologers cannot claim to build on ancient knowledge, but have to change the signs and characteristics over time. They are in turn making the whole concept of Astrology invalid. The real astronomical signs are a few days off from the Sidereal system by now - so not even Sidereal Astrology is using the correct star signs.
Sidereal astrology uses the actual constellation in which the sun is located at the moment of birth as its basis; tropical astrology uses a 30-degree sector of the zodiac as its basis. Tropical astrology is the most popular form and it assigns its readings based on the time of the year, while generally ignoring the positions of the sun and constellations relative to each other. Sidereal astrology is used by a minority of astrologers and bases its readings on the constellations near the sun at the time of birth.
According to some astrologers, the data support the hypothesis that there is a connection between heavenly bodies and human events. There are correlations too synchronous to be mere chance between astrological signs and such things as personality, emotions and human destiny.