Are Database duplication and Mirroring one and the same?
Duplicate Database
It is separate database contains all or subset of the data of Source Database.
Its purpose varies like:

Test backup/recovery procedure
Test upgrade of new release
Test effect of DB performance
Generate reports
Export data table and import in production environment if inadvertently dropped

Snapshot Replication
Here data is replicated at specified time by copying data changes from Source Database (Publisher) to receiving database (Subscriber)
Its purpose varies like:

If data change is infrequent
If database is of small size or data change occurs in large amount