The generations of weak and strong collisionless electrostatic shock waves (CESWs) have been studied by the one-dimensional particle-in-cell simulations in the strong intense laser near critical density plasma interactions. The effects of the ranges of plasma density profiles, non-relativistic and relativistic laser intensities on the generations of CESWs have been explored in the paper. The non-relativistic drive laser generates the weak CESW in laser near critical density plasma interactions with the weak intensity. The electron spectra show double-temperature distributions because the non-relativistic drive laser cannot heat the electrons adequately. The low-temperature electrons have an important influence on the generations of weak CESWs and they also cause that the protons can be accelerated and reflected from the CESWs. The spectra of the weak CESWs protons show a continuously distributed profile. When the range of plasma density up-ramp is large, the process can be observed that the post-soliton structure evolves into the ion acoustic wave and further evolves into the weak collisionless electrostatic shock wave. When the drive laser intensity is relativistic, the electrons are adequately heated to a single relativistic temperature. The effects of the ranges of plasma density profiles on the generations of CESWs have been further analyzed and we found:1) when the range of plasma density up-ramp is large, the potential barrier of ion acoustic wave is shielded by the hot electrons; 2) when the range of plasma density up-ramp is small, the effective distance (i.e., the Debye length) of accelerating field is larger and the endurance time is longer than the case of large plasma density up-ramp range. This makes the ion acoustic wave structure more stable during its forward propagation process. When the velocity difference between the ion acoustic wave accelerating protons and the target normal sheath accelerating protons satisfies the proton reflection condition of CESW, the ion acoustic wave further evolves into the strong CESW and generates monoenergetic protons at the same time.