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An extreme ultra-violet (EUV) wave is characterized as a bright pulse that has emanated from the solar eruption source and can propagate globally in the solar corona.According to one leading theory,the EUV wave is a fast magnetoacoustic wave,as the coronal counterpart of the Moreton wave in the chromosphere.However,previous observations have shown that the EUV wave differs significantly from the Moreton wave in both velocity and lifetime.To reconcile these differences,here we analyze the wave characteristics of a two-fluid MHD model in the stratified solar atmosphere with a height-dependent ionization rate.It is found that the collision between neutral and ionized fluids is able to attenuate the wave amplitude,while causing a slight change in its propagation velocity.Because the chromosphere has the lower ionization rate and the stronger magnetic fields than the corona,the velocity of the Moreton wave is much higher than that of the EUV wave.In contrast to the Moreton waves damped strongly by the collision between neutral and ionized fluids,the EUV wave in the fully ionized corona is able to propagate globally on a time scale of several hours.Our results support the previous theory that fast magnetoacoustic waves account for both EUV and Moreteon waves in the different layers of the solar atmosphere.