The classic would be a geographically distributed datastore with intra-datacenter link being fine, but inter-datacenter being down/degraded. Clients within the datacenter would still be able to talk to the server fine, but server to server inter-datacenter is not going to be OK.

Another part of it is that all hell breaking loose can sometimes look very similar to clean partitions, depending on the network. When network QoS classes are available, what appears to be increased latency or packet loss for one class may be 100% packet loss for the other. Though, you're totally right that all hell breaking loose can be very different - the set of systems that handle flapping & other ugly connection failures well is smaller than the set of systems that handle clean disconnections well :)