Multiple independent studies have confirmed that giant planet occurrence rate increases with host-star metallicity and Jupiters are more common around stars with solar to super-solar metallicity. However, most of these results are derived from the Kepler sample, which is limited to planets within a distance of 1 au from the host star, i.e., hot and warm Jupiters for giant planets. Occurrence rate studies with combined radial velocity and transit surveys show that cold Jupiters beyond 1 au are more common in nature. However, the correlation between the orbital properties of giant planets with host star metallicity is not well understood yet, as most of the studies have been done with samples of small size and metallicities derived from inhomogeneous data. In this work, taking a larger sample of giant planets with host stars properties uniformly derived from Gaia DR3, we show that hot Jupiters are more metal-rich than cold and warm Jupiters. Dividing the planets into high and low eccentricity bins, we show that cold Jupiters have a dichotomy in metallicity distribution, unlike the hot and warm Jupiters: host stars of low eccentric cold Jupiters are relatively metal-poor, on average, with solar metallicity, while host stars of hot Jupiters and high eccentric cold Jupiters are relatively metal-rich, with super solar metallicity on average. Even after considering possible selection effects and biases, our results are statistically significant at 2σ-3σ level. However, from Gaia kinematics, we show that only hot Jupiter hosts are relatively younger than all other Jupiters and represent a kinematically well-separated population. But warm and cold Jupiters have very similar kinematic properties regardless of their eccentricity. We will discuss the exciting implications our results have for Jupiter formation pathways.