Steve Callan at DBASupport has a long artical on What’s in an Oracle Schema?.
While I don’t get this exact question much, I do see that some people get confused between a database and a schema. I create them a schema in a database, give them the user name and password and they think they have a database.
If I ask them if they need a schema or a database they aren’t sure. So usually I just get their requirements and then determine it for myself. Part of being a DBA I guess.
I usually ask them how many uses they need, how much space they need and the number of users or amount of load they are expecting. If it is all pretty low, then they probably only need a schema in an existing database. If they have high demands then their own database might be best.