A fundamental issue in the engineering of coordination models is n coordination abstractions that are correct with respect to the specification of the coordination model they implement. The traditional semantic framework for coordination is focused on describing the admissible evolutions over time of a coordinated system, and is particularly suitable for specifying the laws of a coordination model. On the other hand, formally describing run-time aspects of an implementation requires a different framework, capturing as fundamental idea the interactive behavior of a coordination medium. In this paper, these two frameworks are compared by tackling a crucial issue of coordination models, that is, the conformance of an implementation with respect to a specification. In particular, a definition of conformance is introduced that is shown to be compatible with the standard notion of implementation by horizontal refinement promoted in the context of process algebras. Keywords Semantics of ...