The Zodiac is an imaginary ring in the sky which encircles our solar system like a girdle. To determine the positions of the planets on this circle we need some reference point, a point which will remain fixed while the heavenly bodies keep moving.
The seers of Vedic Astrology took a faraway star which remains stationary and the position of the planets was determined by referring them to this fixed star cluster. This is known as the sidereal system. Sidereal means measured by stars. The fixed star cluster chosen for the purpose is taken as the 1st degree of Aries, the starting point of the Indian Zodiac.
The Western system also uses a fixed reference point but utilizes the equinoxes for the purpose. Interestingly, 1st degree of Aries is yet again the starting point of the Western Zodiac. But the major difference is that the position of the Sun on Vernal equinox (the first day of spring) is taken as the 1st degree of Aries. This works equally well because the Sun moves 360° in a year. This is known as the Tropical Zodiac.
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Taking two different reference points does not make one system valid and the other invalid. In fact, one can be mathematically deduced from the other. Ancient Indians were aware of this. They knew that, because of the perpetual titling of the earth the equinoxes moved approximately 1° in every 72 years. So, they introduced the idea of 'Ayanamsha' to accommodate the procession of the equinoxes (Ayanchalan).
Hence, the Western Tropical Zodiac is called 'Sayan' (with Ayan) i.e., with the procession of equinoxes and the Sidereal Zodiac is called 'Nirayan' (without Ayan) where this is ignored.
The planets and the houses in both systems are the same. There are some differences in approach. For example, in Indian Astrology the most important reference point in a Horoscope is the 1st house known as Ascendant while in the Western System the Sun occupies the central place.