Why are there so many DFT Methods?
The issue is that unlike for the methods based on Hartree-Fock, there isn't a systematic path to improving DFT. Unlike for HF, where we can treat the correlation as a pertubation (MP-n) or include excited Slater determinants (CI and CC) to generally improve our description of a molecule, we still don't have a way of determining the true form of the density functional (specifically the part governing exchange correlation) in DFT, so for now we use educated guesses for the general form (Local Density Approximation, Generalized Gradient Approximation, etc) and optimize them for specific systems. 

In principle, if the exact form of the functional were known, DFT would be exact. This is why some authors like to use a separate term DFA (Density Functional Approximation) to describe the instances of DFT in use today.