What are energies in computational methods relative to?
Ab initio calculations give the absolute energy of the system of fixed nuclei and moving electrons (all considerations on the type of calculations are implicit such as the Born-Oppenheimer approx.). There isn't any distinction of concepts of absolute energies between softwares when ab initio methods are employed (no ambiguity is allowed as pointed out by Pentavalentcarbon). Maybe the confusion can be illustrated with an example: you can't obtain heats of formation, as an absolute energy, from an ab initio calculation but it serves as a good approximation depending on the method.