What does SQL Server Error 3154 really mean?

Error 3154: The backup set holds a backup of a database other than the existing database.

I recently taught a class and one of my students encountered this error message.  I thought others might want to know the answer to this puzzle as well.

The error message, in this case, was really misleading.  It happened while attempting to restore the master database.  The answer is really simple:

Use the REPLACE keyword in your RESTORE statement.

Example:

RESTORE DATABASE YourDB
FROM DISK = 'C:\YourDB.bak'
WITH REPLACE

As you can see the Error message doesn't quite lead you in this direction.  But it will work. 

Good luck.  Have a blessed day!