The dynamics of bubble clouds induced by ultrasound field are investigated in a regime where the cloud size is much smaller than the ultrasound wavelength. Two frequently used models describing the dynamics of individual bubbles inside a bubble cluster in an acoustic field are studied, one based on the homogeneity assumption, and the other based on the simultaneous motion assumption. A modified formula of the homogenization-based model is presented, and an inherent distinction in bubble-bubble interaction term is found in comparison to the simultaneous motion model. To gain insight into the mechanisms of such distinction, a reduced model unifying these two models is presented, and such distinction is explained by the spatial dependence of the bubble-bubble interaction in a bubble cluster accordingly. To validate the reduced model, the normalized distance γbb and the cloud interaction parameter B0 are used as two scaling parameters, and the comparison between the present model and the coupled Rayleigh-Plesset type equations is made. A conclusion is that, in the weak bubble-bubble interaction case (γbb>10), the reduced model can well reproduce the radial motion of bubbles in the cluster during the growth stage and the collapse stage in each acoustic cycle; in the strong bubble-bubble interaction case (γbb<10), the growth phase of bubbles in the cluster can be accurately predicted by the reduced model only if B0 or the amplitude of driving field is small.