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Two paradigms dominate this space: Schema-Guided Dialogue (SGD), a research framework for zero-shot API generalization, and the Model Context Protocol (MCP), an industry standard for agent-tool integration. While both enable dynamic service discovery through schema descriptions, their formal relationship remains unexplored. Building on prior work establishing the conceptual convergence of these paradigms, we present the first process calculus formalization of SGD and MCP, proving they are structurally bisimilar under a well-defined mapping Phi. However, we demonstrate that the reverse mapping Phi^{-1} is partial and lossy, revealing critical gaps in MCP's expressivity. 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