In this article, we identify a subclass of Timed Automata (Alur and Dill \citeAlurDill: [1], called Timed State Machines as weakly equivalent w.r.t. strongly timed behavior to a canonical class of Time Petri Nets (TPNs) in the sense of Merlin and Farber [17]; more precisely, the weak equivalence holds for bounded non-Zeno TPN with self-concurrency 1, denoted N1TPN. TSMs, and in particular message synchronized products, called TIOSMs, are mainly used for test generation; on the other hand, there is a rich literature on TPNs in verification. Hence our motivation to combine the strengths of both models. We present here an explicit construction for two - way translation between 1-TPNs and TSMs; in both directions, the power of clock timing is exploited to obtain concise and analyzable models. The TSM model obtained from the translation has a state set the size of the reachability graph; it thus improves on the class graph obtained by the enumerative method [3],[2]. The existence of the translation procedure, which has also been implemented in a tool prototype, XTIOSM, makes the model equivalence effective.