One sky, two starting points
Both systems split the sky into twelve signs, but they mark the start of Aries differently. Western ties it to the spring equinox; Vedic ties it to the visible stars. The difference has grown to about 24 degrees — the ayanamsa. This is the single reason your 'sun sign' can change between systems.
What Vedic astrology does best
Timing. The vimshottari dasha system assigns periods of life to planets, and transits (gochar) — especially Saturn and Jupiter — are read against the natal Moon. Sade Sati, dasha changes and muhurat selection are all Vedic strengths. If your question is 'when', Vedic is the answer.
What Western astrology does best
Character and cycles. The natal chart as a psychological mirror, progressions that show inner growth, and the slow outer-planet transits that mark generational change. If your question is 'who am I and how do I grow', Western methods speak plainly.
Using both, without confusion
Keep the two charts side by side with different jobs: Western for self-understanding, Vedic for decisions and dates. Astrologer Inside generates both from one set of birth details, so you never have to pick a side — you just pick the right tool for the question you are asking today.