Kimon wants to describe traffic sent between servers in his data center. What common terminology should he use to describe this?

Traffic sent between systems in the same data center is called east/west traffic since it does not flow across network boundaries. East/west traffic requires additional design work in many organizations if monitoring and other security is desired. Traffic that is external to the data center, either inbound or outbound, is called north/south traffic. Privileged/unprivileged and store/forward are not typically used to describe the traffic flows in the question.