Asynchronous communication encompasses a variety of fea-tures besides the decoupling of send and receive events. Those include message-ordering policies which are often crucial to the correctness of a distributed algorithm. This paper establishes a map of communica-tion models that exhibits the relations between them along two axes of comparison: the strength of the ordering property and the level of ab-straction of the specification. This brings knowledge about which model can be substituted by another without breaking any safety property. Fur-thermore, it brings flexibility and ready-to-use modules when developing correct-by-construction distributed systems where model decomposition exposes the communication component. Both criteria of comparison are covered by refinement. We consider seven ordering policies and we model in Event-B these communication models at three levels of abstraction. The proofs of refinement between all of these are mechanized in Rodin.