The symmetry-adapted-cluster (SAG) and SAG-configuration interaction (SAC-CI) many-body theories have been applied to calculate, within the all-electron ab initio Hamiltonian, the singlet ground and excited states of MoF6 and MoOF4. Chemical bonding and electron correlation are quite important to reduce the formal charge of electrostatic Mo-ligand bonds in both ground and excited states. The calculated excited states are all characterized as electron-transfer excitations from ligands to molybdenum, reducing the ionicity of the Mo-F bonds. For MoF6, we assign the energetically lower three peaks to dipole-allowed electronic transitions to the T-1(1n), excited states, consistently with the calculated oscillator strengths, and at variance of the previously proposed assignments. The fourth and fifth peaks, having very weak intensity, have been tentatively assigned to the dipole-forbidden 2(1)E(g) and 4(1)T(2g) excited states, respectively. The experimental excitation energies and intensities are well reproduced by the present calculations. The maximum discrepancy (0.35 eV) of the calculated excitation energies occurs for the first peak. Chemical bondings of MoOF,I in the ground and excited states, although exhibiting great reductions of the ionicity, are more ionic than those of MoF6. For the visible-UV spectrum of MoOF4, we assign the two experimental peaks to dipole-allowed transitions to the E-1 excited states. The present assignments of the observed electronic transitions based on the accurate SAC-CI calculations should be more reliable than the previous ones. We further used the frozen-orbital-analysis (FZOA) method in order to understand and rationalize the energy orderings and splittings for the excited states having the same excitation nature. We confirm that the FZOA method is very simple and useful to examine and explain the origin of the orderings of the excitation levels. Some relationships on the orderings and splittings presented here should be of general applicability to any systems.