Rashi and Moon sign: the difference
A rashi is any of the twelve signs. The Moon sign is the rashi that the Moon occupies at a given moment, and it is a specific use of the rashi system.
What it is
Every person has a Moon sign, found from the Moon's sidereal longitude at birth. The Moon sign is different from the Lagna, which is the rising sign at the moment of birth.
How it is worked out or read
In the tools, the Moon sign is shown beside the Lagna and in the panchang for the day. Readings that use the Moon sign alone are a separate tradition.
Where it appears on this site
The Moon sign is in the birth chart. See the Moon chart.
What 'your rashi' means
In everyday Indian usage, when someone asks 'what is your rashi?', they mean the Moon sign, the sign the Moon occupied at birth. Newspaper horoscopes in India are usually arranged by Moon sign, the naming syllables come from the Moon's nakshatra, and the Vimshottari dasha begins from it. In Western usage, by contrast, 'your sign' means the Sun sign. This difference is the source of much confusion when people compare Indian and Western readings.
Three signs in every chart
Every chart has at least three important signs: the Lagna, the rising sign; the Moon sign, or chandra rashi; and the Sun sign, or surya rashi. Jyotish gives the Lagna and the Moon sign the most weight, and some readings are made from both, a chart counted from the Lagna and another counted from the Moon. The Sun sign matters too, but less often stands alone as a person's 'sign'.
Finding yours
The planet table on the birth chart page shows the sign of the Moon and the Lagna. The Moon sign is usually reliable even without an exact birth time, since the Moon spends about two and a quarter days in each sign; only births near a sign change need a precise time. The Lagna, by contrast, changes about every two hours and needs a good birth time.
Two uses of the word
The word rashi refers to any of the twelve signs, while the Moon sign refers to the rashi that the Moon occupies at a given moment. The first is a category, and the second is a specific fact about a chart. A person's Moon sign is one of the twelve rashis, but it is not a separate kind of thing. Keeping this clear helps a reader avoid asking whether a rashi is a personality, when the question should be which sign the Moon was in.
Using the Moon sign in the chart
The Moon sign is read beside the Lagna. Where the two are different, the reader has two sign-based reference points, one for the body and first house (Lagna) and one for the mind and emotions (Moon). Many rules use the Moon sign for counting houses, and the Sade Sati check starts from the natal Moon sign. The site's tools always show both, so that the reader can see which one a rule uses.