Organic-inorganic coupling in the hybrid lead-halide perovskite is a central issue in rationalizing the outstanding photovoltaic performance of these emerging materials. Here, we compare and contrast the evolution of the structure and dynamics of hybrid CH3NH3PbBr3 and inorganic CsPbBr3 lead-halide perovskites with temperature, using Raman spectroscopy and single-crystal x-ray diffraction. Results reveal a stark contrast between their order-disorder transitions, which are abrupt for the hybrid whereas smooth for the inorganic perovskite. X-ray diffraction observes an intermediate incommensurate phase between the ordered and the disordered phases in CH3NH3PbBr3. Low-frequency Raman scattering captures the appearance of a sharp soft mode in the incommensurate phase, ascribed to the theoretically predicted amplitudon mode. Our work highlights the interaction between the structural dynamics of organic cation CH3NH3+ and the lead-halide framework, and unravels the competition between tendencies for the organic and inorganic moieties to minimize energy in the incommensurate phase of the hybrid perovskite structure.