A technique for managing synchronous replication and asynchronous replication of both block-based objects and file-based objects employs a common replication session manager configured from a common GUI application. The replication session manager can access different settings for different data objects (e.g., LUNs, file systems, block-based vVOLs (virtual volumes), file-based vVOLs, VMDKs, etc.), with replication settings maintained on a per-data-object basis. The replication session manager can also orchestrate synchronous and/or asynchronous replication sessions, failover, and/or recovery, for any given data object in accordance with the particular data-object-specific settings established for that object.