Multiarm star polymers represent a valuable model system for investigating the dynamics of tethered chains, spherical brushes, or grafted colloidal spheres. Because of their topology, the multiarm stars exhibit a nonuniform monomer density distribution leading to a core-shell morphology, which is responsible for their rich dynamic structure. When the stars interpenetrate, they exhibit liquidlike (macrocrystalline) order due to the enhanced osmotic pressure which balances the entropic stretching of the near-core segments and the excluded volume effects. Using dynamic light scattering, we probe three relaxation modes in the semidilute regime: (i) the fast cooperative diffusion, which is characteristic of their polymeric nature (entangled shell arms); (ii) the self-diffusion of the stars (essentially cores), probed because of finite functionality polydispersity, as confirmed by independent pulsed-field gradient NMR measurements; and (iii) the structural mode, which corresponds to rearrangements of the ordered stars. We develop a mean-field scaling theory, which captures all features observed experimentally with good quantitative agreement. The two slow modes, ii and iii, are reminiscent of the behavior of interacting hard colloidal spheres and are governed essentially by the same physics. We propose these model soft spheres as appropriate vehicles for unifying the descriptions of the dynamics of polymers and soft colloidal dispersions.