A person can be one sign in a Western chart and a different one in an Indian chart. The discrepancy has a precise astronomical cause and a long history of debate.
The two systems anchor to different things
The tropical zodiac is defined by the seasons, beginning at the moment of the spring equinox regardless of which stars lie behind the sun.
The sidereal zodiac is defined by the stars, keeping the signs aligned with the constellations that originally gave them their names.
Both are internally consistent. They measure from different starting points, so they necessarily produce different results.
Precession opened the gap slowly
The earth's axis traces a slow circle over roughly twenty-six thousand years, shifting the equinox point gradually against the background stars.
When the zodiac was standardised in antiquity the two systems coincided closely, and they have drifted apart at about one degree every seventy-two years since.
The accumulated difference is now roughly the width of a whole sign, which is why the two systems commonly disagree by exactly one.
Each tradition made a defensible choice
Western practice retained the seasonal anchor, on the reasoning that the signs describe qualities associated with the seasonal cycle rather than with particular stars.
Indian practice retained the stellar anchor, keeping the signs tied to the constellations and to a system of lunar mansions that depends on stellar positions.
Neither is a mistake within its own framework, since the two are measuring different things and were never claiming to measure the same one.
The offset itself is disputed
Converting between the systems requires a value for the accumulated difference, and that value depends on when the two are held to have coincided.
Several competing values are in use, differing by a degree or more, which produces different sidereal charts for the same birth.
The disagreement persists because the original coincidence date is not recoverable from surviving evidence with the precision the question requires.
The constellations complicate matters further
Astronomical constellation boundaries are unequal in width, so the sun spends unequal periods in front of each and passes through one not included in the zodiac at all.
Both zodiacs use twelve equal thirty-degree divisions, which are conventions of measurement rather than descriptions of the sky.
Arguments that the whole scheme is wrong because the sky does not match usually conflate the measuring convention with the constellations that named it.