Kripke Structures (KSs) and Labelled Transition Systems (LTSs) are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find manyad hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in KSs and divergence-sensitive branching bisimulation in LTSs. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimization techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences.