Numerous studies of integrated starlight, stellar counts, and kinematics have confirmed that the Milky Way is a barred galaxy. However, far fewer studies have investigated the bar's stellar population properties, which carry valuable independent information regarding the bar's formation history. Here, we conduct a detailed analysis of chemical abundance distributions ([Fe/H] and [Mg/Fe]) in the on-bar and off-bar regions to study the azimuthal variation of star formation history (SFH) in the inner Galaxy. We find that the on-bar and off-bar stars at Galactocentric radii 3 kpc < r(GC) < 5 kpc have remarkably consistent [Fe/H] and [Mg/Fe] distribution functions and [Mg/Fe]-[Fe/H] relation, suggesting a common SFH shared by the long bar and the disc. In contrast, the bar and disc at smaller radii (2 kpc < r(GC) < 3 kpc) show noticeable differences, with relatively more very metal-rich ([Fe/H] similar to 0.4) stars but fewer solar abundance stars in the bar. Given the three-phase star formation history proposed for the inner Galaxy in Lian et al., these differences could be explained by the off-bar disc having experienced either a faster early quenching process or recent metal-poor gas accretion. Vertical variations of the abundance distributions at small rGC suggest a wider vertical distribution of low-a stars in the bar, which may serve as chemical evidence for vertical heating through the bar buckling process. The lack of such vertical variations outside the bulge may then suggest a lack of vertical heating in the long bar.