We analyze atomic structures of plasma embedded aluminum (Al) atom and its ions in the weakly and strongly coupling regimes. The plasma screening effects in these atomic systems are accounted for using the Debye and ion sphere (IS) potentials for the weakly coupling and strongly coupling plasmas, respectively. Within the Debye model, special attention is given to investigate the spherical and non-spherical plasma-screening effects considering in the electron-electron interaction potential. The relativistic coupled-cluster (RCC) method has been employed to describe the relativistic and electronic correlation effects in the above atomic systems. The variation in the ionization potentials (IPs) and excitation energies (EEs) of the plasma embedded Al ions are presented. It is found that the atomic systems exhibit more stability when the exact screening effects are taken into account. It is also showed that in the presence of strongly coupled plasma environment, the highly ionized Al ions show blue and red shifts in the spectral lines of the transitions between the states with same and different principal quantum numbers, respectively. Comparison among the results obtained from the Debye and IS models are also carried out considering similar plasma conditions.