Atomic Multicast is a group communication method in which exact copies of a single message are sent to a group of receivers, and mechanism guarantees that message is received either by all of receivers or none of such.
Example of use: Replicated Stateful Services Fault Tolerance mechanism requires Atomic Multicast for synchronization.
Reliable Multicast is a group communication method in which effort is made for delivering exact copies of a single message to all of receivers in a group, but mechanism does not guarantee it. It is possible for a message to reach only part of receivers.
Example of use: Reliable Multicast is often enough for finding Distributed Objects of a given type, if we are not too selective.
See: Broadcast and Multicast routing, Group Communication in Distributed Systems, AI, Stateful, Stateless, Services.