The main difference lies in how we divide the sky: zodiac signs are twelve equal 30-degree segments of the ecliptic—the Sun’s apparent yearly path across the celestial sphere—while zodiacal constellations are physical groups of stars with irregular shapes and sizes defined by modern astronomy.
While the Sun spends exactly the same amount of time in each "sign," it stays in actual constellations for varying periods, ranging from 45 days in Virgo to only 7 days in Scorpius. Furthermore, due to the Earth's axial wobble called precession, these two systems have drifted apart over the centuries; today, the Sun even passes through a thirteenth constellation, Ophiuchus, which is not represented in the traditional twelve-part division of the Sun's path.