the conception of schema is different in different db software.
here i just refer to oracle schema。
following is quote from "http://docs.oracle.com/cd/B19306_01/server.102/b14200/sql_elements007.htm"
schema conception:
Schema Objects
A schema is a collection of logical structures of data, or schema objects. A schema is owned by a database user and has the same name as that user. Each user owns a single schema. Schema objects can be created and manipulated with SQL and include the following types of objects:
Clusters
Views
Nonschema Objects
Other types of objects are also stored in the database and can be created and manipulated with SQL but are not contained in a schema:
Contexts
Directories
Parameter files (PFILEs) and server parameter files (SPFILEs)
Profiles
Roles
Rollback segments
Tablespaces
Users
here we know that the database include schema objects and non-schema objects.
Schema objects are logical data storage structures. Schema objects do not have a one-to-one correspondence to physical files on disk that store their information. However, Oracle stores a schema object logically within a tablespace of the database. The data of each object is physically contained in one or more of the tablespace's datafiles. For some objects, such as tables, indexes, and clusters, you can specify how much disk space Oracle allocates for the object within the tablespace's datafiles.
There is no relationship between schemas and tablespaces: a tablespace can contain objects from different schemas, and the objects for a schema can be contained in different tablespaces.