FSMO Roles Configuration | Windows Server | Yovan Sanghvi

Child Domains: Exist within the same Active Directory forest as the parent domain. They share the same schema, configuration, and Global Catalog (GC). Since a DC in the parent domain already has a complete picture of the forest [THEREFORE THEY ARE NOT PRESENT IN THE CHANGE DOMAIN CONTROLLER OPTION]
Trusted External Domains: Are separate forests with a trust relationship established for authentication purposes. ADUC needs to contact a DC in the trusted domain to verify user/group information, hence the option to switch to a trusted domain controller in the change domain controller.