Vedic and Western
Your Sun sign is the zodiac sign the Sun was passing through, from Earth's point of view, on the day you were born. It's the placement most people mean when they ask "what's your sign," and it's the only one of the major three that doesn't need your birth time to calculate, just the date.
In astrology, the Sun is generally read as your core identity: the version of you that's consistent across situations, and the qualities you're working toward expressing more fully over your life.
The zodiac is divided into 12 roughly month-long segments, corresponding to the tropical positions the Sun moves through over the year. We calculate the Sun's exact tropical longitude for your birth date and map it to the segment it falls in. Near a sign's start or end date, the exact year matters, since the Sun doesn't cross into the next sign on precisely the same calendar day every year.
The Sun sign is your headline. The Moon sign is your emotional interior. The Ascendant is your outward first impression, calculated from your birth time and location rather than the date alone. A full birth chart reads all three together, plus the other planets, rather than any one in isolation.
Western astrology uses the tropical zodiac, which is anchored to the seasons rather than to fixed background stars. Aries always begins at the spring equinox in the Northern Hemisphere, regardless of where the constellations have drifted to over the centuries. This is different from the sidereal zodiac used in Vedic astrology, which does track the visible constellations. Neither is more "correct," they're two different reference systems.
Usually a time zone issue. If you were born close to a sign's start or end date, the exact moment of the Sun's sign change (often calculated in UTC) can shift your sign depending on which time zone a site assumes for your birth date. Using your correct birth date and location avoids this.
It's the most commonly known, but not necessarily the most psychologically significant. Many astrologers weigh the Ascendant and Moon sign just as heavily, sometimes more, depending on the chart.
They use different zodiac systems: tropical (Western) versus sidereal (Vedic). The sidereal zodiac is offset from the tropical one by roughly 24 degrees today, which can shift a placement into the neighboring sign. Neither calculation is wrong, they're answering the question differently.