Our Jr. DBA ran to me with this error just a few days ago while restoring the database.
Error 3154: The backup set holds a backup of a database other than the existing database.
Solution is very simple and not as difficult as he was thinking. He was trying to restore the database on another existing active database.
1) Use WITH REPLACE while using the RESTORE command. View Example
2) Delete the older database which is conflicting and restore again using RESTORE command.
I understand my solution is little different than BOL but I use it to fix my database issue successfully.
3) Sample Example :
RESTORE DATABASE AdventureWorks
FROM DISK = 'C:\BackupAdventureworks.bak'
Reference : Pinal Dave (https://blog.sqlauthority.com)