A zodiac is a system of measurement, just as the metric system of lengths, weights,volumes is a system of measurement.
The metric system has a counterpart (a different system of measurement) in the English system.
Both systems measure things accurately, within that system, and a measurement from one system can be translated into the other. For example, one meter is the same as 39.37 inches.
The two commonly used zodiacs, the tropical and the sidereal, are two systems of measuring the sky for purposes of locating celestial bodies. The difference in the two systems is their point of beginning.
The tropical zodiac begins (0 Aries) at the place in the sky where the center of the Sun crosses the celestial equator at the beginning of the northern spring each year (the vernal equinox). It is observed and measured by astronomers annually.
The sidereal zodiac begins at a point believed to have been the vernal equinox on some given date in the distant past, when astrology was in its infancy. Its point of beginning is fixed in the heavens (is the same as a fixed star). As of this moment, using the Lahiri Ayanamsa (the official ayanamsa of India), the sidereal zodiac is 24 degrees and 3 minutes earlier in the signs than the tropical zodiac. There are different ayanamsa (Fagan, Krishnamurti, Raman, etc.) which vary slightly in their point of beginning. If your Moon is at 18 Leo 38 in tropical, you will find it at 24 Cancer 35 in sidereal (Lahiri). (5-18-38 minus 23 deg 03 min = 4-24-35). The separation of the two points of beginning (0 Aries) increases slightly with the passing years (about 1 degree every 70 years); in other words, 70 years ago, the difference between the two was about 23 degrees rather than the current 24. On 10 August 1943, the difference was 23 d 04 m. [Lahiri])
Both systems work. Both systems take the Precession of the Equinoxes into account (many sidereal astrologers will disagree with me here, but that is because they have not thought out the problem.) But each system must be taken and used on its own terms. To translate from one zodiac to the other is not so simple as converting from the Metric to the English system, because not only is there a quantitative value, but also a qualitative one (the "meanings" of sign, or of specific degrees).
The tropical zodiac is the one used by most western astrologers. The sidereal zodiac is used by the Vedic astrologers (Indian). The two systems of astrology, while sharing most of the fundamentals, differ greatly in method. I would suggest to beginning students of astrology that they arbitrarily choose one system or the other and work within its confines. Once the student gains proficiency in the fundamentals and basic methods of the chosen system, then the other system may be profitably explored without causing confusion.
Let's assume that a person has a tropical Ascendant of 12 Cancer 28. Then, subtracting 24 d 03 m, we find that in the sidereal zodiac the Ascendant falls in 18 Gemini 25. First, if the Ascendant represents "personality" [physical constitution, appearance, behavioral presentation], then we should be able to see which description -- Gemini or Cancer -- best fits the actual person; the two signs are quite different in their qualities and characteristics. Second, the lord of Gemini is Mercury and the lord of Cancer is Moon. These two planets will probably be posited in different signs and houses in the given chart, and behold different aspects and other conditioning. So, with some study of a particular chart -- of a person whose character is well understood -- the astrologer should be able to decide (at least on this basis) which of the two zodiacs seems to be "the correct one."
Also, in about 80% of all instances, the signs on the house cusps will change (use whole sign houses for this experiment, to simplify). This means the lords of the houses will also change. This should result in very different readings for the affairs of the houses. If you have already acquired basic skill in chart interpretation, I invite you to try this experiment with three or four charts. You may be very surprised by what you discover.