Hi, DFTB tries to approximate DFT by using a minimal basis set, nearest neighbor and pre-calculated matrix elements (Slater-Koster tables). That's essentially DFTB, or 'DFTB0'. DFTB2 or SCC-DFTB includes a self-consistent charge step, optimizing the (Mulliken) charges. Third order DFTB, or DFTB3 includes an additional polarization term. There are a few good review articles around.