The DMI (Datatel Messaging Interface) is a message queue and broker protocol that communicates between DMI Listeners and other Colleague utilities, including the the DMI Registry. Some forms/screens that interact directly with the DMI protocol/messagebus, DMI Registry, or DMI Listeners are named as such (DRUS, DPWP...).
DMI Listeners are Java-based programs that interpret commands between two software components that do not have a common command set, such as LDAP and DMI to provide user logins via LDAP.
From the standpoint of DMI itself, the DMI Registry is named as such because it contains records that are often pulled from, synced with, or authenticated by DMI Listeners. I do not believe Colleague uses the DMI internally for the Registry. Not sure of the history around this naming scheme.