In real both of them are telling band gap in material But you should see that x and y axis start from zero and always first tangent is taken.

The Tauc plot can give you the well defined bandgap that is defined as the energy difference between the lowest conduction band a highest valance band state. However, it gives you an approximate energy you can expect to have significant optical absorption, and this value depends on the thickness of the sample. For instance, if you get 10% absorption at 2 eV with a 100 nm thick film, you can get 10% absorption at maybe 1.95 eV with a 1000 nm thick film. The Tauc would give different bandgaps of 2 eV and 1.95 eV, respectively, for the same material but different thickness.

There are better way to get more a meaningful bandgap. See this paper (DOI： 10.37188/CJL.EN20240013) for the discussion about the differences between the single particle bandgap, excitonic bandgap, Tauc-plot bandgap, typically decreasing in the order, as well as the bandgap derived from a modulation spectroscopy technique.

Nazanin Hamnabard Use the tangent that fits the linear portion of the absorption edge (green line) and extrapolate it to the photon-energy axis to obtain Eg. The black tangent lies in the sub-gap/Urbach tail and will underestimate the band gap. Always ensure the vertical axis is (αhν)γ with the correct (γ)gamma for direct or indirect transitions before extracting Eg.