Two aspects, aside from the imprecisions that Gabriel Ravanhani Schleder already adressed properly:
1) If the material has an indirect bandgap, i.e. the highest valence and the lowest conduction band location are at different locations in the k space, you cannot directly excite that. The optical bandgap is the minimum difference of bands at the same k space location which is equal to the electronic one only for a direct bandgap.
2) You mention "DFT": DFT is only an approximation and there is no systematic law whether the bandgap from there will be larger or smaller than the experimental one, that is only determined by benchmark. However, aspect 1) stays valid if you look at calculated band gaps.