What differences between
             Western astrology and Jyotish? 

There are five main differences: 
1 - Indian astrology (Jyotish) takes into account in the calculation of the astral chart, the precession of equinoxes called "ayanamsa". It is an astronomical parameter related to the rotating shaft of the Earth on itself, or libration. Few western astrologers make use of it ; this distorts the calculations of the true positions of planets and houses. 
2 - Indian astrology uses only the visible material bodies to a naked eye, in the solar system: Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. It is due to the fact that in ancient times, the Rishis (great sages of the ancient India), like Parashara for example, laid the foundations of Jyotish, there was no telescopes ! In Jyotish we also take into account two mathematical points (non material) related to the orbit of the Moon. These are Rahu and Ketu, they are treated like "virtual" planets in calculations and interpretations. Few western astrologers are making use of them. In western astrology, there names are "Head of the dragon" and "Tail of the dragon". Later on, the western astrologers added the planets that have been discovered because of the progress of astronomy: Uranus, Neptune and Pluto. But the interpretations about them stay controversial. 
3 - An astral chart drawn according to Jyotish, is grounded on the ascendant. That is to say, on the sign of the zodiac that is rising up (that is in ascension) on the horizon at the moment and place of the birth. For this reason, the birth time is very important. The western astrology is rather based on the zodiacal sign of the Sun. 
4 - In Jyotish, one gives a significant importance to the position of the Moon which is taken into account like a secondary ascendant. The western astrology, is rather based on the position of the Sun. 
5 - Jyotish, uses secondary and specialized birth charts, called Vargas. Each one of them gives some details on a particular aspect of life: spouse (or husband), siblings, parents, children, success, family happiness, etc.