I head that Planets and nakshatra's are entirely different things in Indian astrology. Is that right? But I think in modern astronomy (science), Planet and nakshatra are related. Can anyone tell how Planet and nakshatra are related to or different from each other?
Nakshatras are 27 (or 28) divisions of sky. They correspond to the space the moon travels in one day. That's why they are called lunar mansions. They each have a type of Shakti, that corresponds to the God it is associated with. Look at the Wikipedia article for more info on nakshatras. The planets are the planets in orbit. Vedic astrology considers the sun, moon, mars, mercury, jupiter, venus, and saturn to be the main planets. There are also two nonphysical planets, Rahu and Ketu. Please read more about Vedic astrology.
Astrology considers seven planets Sun, Moon, Mercury, Mars, Venus, Jupiter, Saturn and two nodes Rahu and Ketu. Since astrology is study of planetary influence viewing them from earth constellation or Zodiac becomes reference frame. Each constellation consists of group of stars called Nakshatra.
In Vedic astrology Moon sign is calculated based on Moon transition through different constellation, so based on placement of Moon on a particular nakshatra Moon sign will be calculated.
Please read our article "Zodiac - Frame of Reference in Astrology" for more understanding