For Oracle, we mount the instance to the database or mount the database to the instance?
We are mounting a database to an instance. See the concepts guide:


  The instance mounts a database to
  associate the database with that
  instance.


One way I've seen it explained (probably here or on SO) is that the instance is the memory structures and processes, and the database is the data on disk. The instance has to have a database associated with it to be able to do anything useful.