My CS teacher doesnt want to give me marks for saying that multiple databases can be stored in a single file. He agrees that its possible, but not "normal". I need some real-world, "its-been-done" examples to prove that its not such an exception, and thus claim some marks back.
By traditional definition, I think it would be fair to say that a 'database' is a collection of related information objects... with emphasis on the word related.
Within a database, one can have many, many tables, queries, procedures, etc. Some tables can end up being quite diverse and unrelated.
For instance, I might have a database for my company that keeps track of everything the goes on. There can be sales tables, customer tables, raw material tables, employee tables, and on, and on, and on. In the end, ALL those tables have something to do with my company, and together they form my company database. Individually, the employee table may have nothing in common with the raw materials table.
Having said this... I think the answer to your question is largely a question of semantics rather than actual practice. In reality, even though a database is generally viewed as a single object (or file)... it is actually composed of many individual elements. One could, I suppose, have an employee database, a products database and a sales database all defined within a single SQL SERVER database called MYCOMPANY... but I think this is simply splitting hairs.
I don't know if this answers your question or not...