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In this paper, we introduce a common semantic framework for developing and formally modeling use cases and task models. Use cases are the notation of choice for functional requirements specification and documentation, whereas task models are used as a starting point for user interface design. Based on their intrinsic characteristics we devise an intermediate semantic domain for use cases and for task models, respectively. We describe how the intermediate semantic domain for each model is formally mapped into a common semantic domain which is based on sets of partial order sets. We argue that a two-step mapping results in a semantic framework that can be more easily validated, reused and extended. As a partial validation of our framework we provide a semantics for ConcurTaskTrees (CTT) one of the most popular task model notations as well as our own DSRG use case formalism. Furthermore we use the common semantic model to formally define a satisfiability relation between task model and use case specifications.