Vedic astrology, Jyotisha, the science of light, shares an ancestry with Western astrology and diverges from it at several specific points. Naming the divergences is the quickest way to describe it.
The zodiac is sidereal. Signs are measured against the fixed stars rather than from the equinox, and the difference between the two frames, the ayanamsha, is currently around twenty-four degrees and grows by about a degree every seventy-two years. In practice this means most people's Sun sign in a Vedic chart is the one before their Western one. Which ayanamsha value to use is itself unsettled, with the Lahiri value official in India and several others in use.
The Moon, not the Sun, is the primary light. A Vedic chart is read from the Moon's position and from the ascendant far more than from the Sun, and the Moon's Nakshatra, one of twenty-seven lunar mansions dividing its monthly path, is treated as more personally defining than the sign.
There are nine planets, the Grahas: the Sun, Moon, the five visible planets, and Rahu and Ketu, the north and south lunar nodes, which are points rather than bodies and carry heavy interpretive weight. Uranus, Neptune and Pluto are not classically used.
The timing system is the great technical difference. Vimshottari Dasha allots the years of a life to planetary periods and sub-periods in a fixed sequence of 120 years, starting from the Moon's Nakshatra at birth, so that a chart yields a dated sequence rather than a general tendency. Western astrology has nothing of comparable specificity in standard use.
Divisional charts, the vargas, subdivide each sign to examine particular matters, the ninth division for marriage and fortune, the tenth for career, and are read alongside the main chart.