We perform molecular dynamics simulations to compare the structures and dynamics of a simple and a polymerized ionic liquid. The latter comprises [BF4] anions and [(CH2)6-C3H3N2]25 cations and, hence, the charged imidazolium rings are, unlike in most previous studies, embedded in the polymer backbone rather than in side chains. It is found that cation polymerization weakly affects the local structure but leads to a strong slowdown and an enhanced heterogeneity of the dynamics. Despite strongly different diffusion coefficients of the anions and polymerized cations, reflecting single ion conductor behavior, the structural relaxation of the anions remains coupled to the segmental polymer motion. A comparison with literature results indicates that polymerized cations with embedded and pendant imidazolium rings exhibit different anion association and cause different anion transport mechanisms, with prevailing diffusive and hopping motions, respectively. In addition, we observe that the Rouse model reasonably well describes the polymer dynamics in our case of charged chains strongly interacting with counterions. Specifically, it captures the static amplitudes and time constants of the lower Rouse modes, while there are strong deviations from the model predictions for the higher Rouse modes, which are associated with smaller length scales and sensitive to structural and dynamical heterogeneity related to polycation-anion association.