For a variety of plasma conditions a comparison is made between three standard models of ionization equilibrium, namely corona, local thermodynamic, and collisional radiative equilibrium, respectively. Through the use of examples and illustrations it is shown that for the same plasma conditions and identical level structure and rate coefficients, the different models predict widely varying results that can significantly affect such important plasma properties as charge state, transport coefficients, energy transport, magnitude and distribution of the emitted radiation, and various features of diagnostic value. Also, the frontside emission spectra from a laser target interaction is shown for a variety of standard approximations including optically thick and thin, with and without inner shell opacities, and Rosseland mean opacities. The results show the consequences of these approximations and their effects on the emitted spectra. Finally, a discussion is given on the various effects that a dense plasma environment has on atomic structure and atomic processes including level shifts, ionization lowering, collision cross sections, and collision widths.