Every instance of a running PostgreSQL server manages one or more databases. Databases are therefore the topmost hierarchical level for organizing SQL objects ("database objects"). This chapter describes the properties of databases, and how to create, manage, and destroy them.
A database is a named collection of SQL objects ("database objects"). Generally, every database object (tables, functions, etc.) belongs to one and only one database. (But there are a few system catalogs, for example pg_database, that belong to a whole installation and are accessible from each database within the installation.) More accurately, a database is a collection of schemas and the schemas contain the tables, functions, etc. So the full hierarchy is: server, database, schema, table (or something else instead of a table).
An application that connects to the database server specifies in its connection request the name of the database it wants to connect to. It is not possible to access more than one database per connection. (But an application is not restricted in the number of connections it opens to the same or other databases.) It is possible, however, to access more than one schema from the same connection. Schemas are a purely logical structure and who can access what is managed by the privilege system. Databases are physically separated and access control is managed at the connection level. If one PostgreSQL server instance is to house projects or users that should be separate and for the most part unaware of each other, it is therefore recommendable to put them into separate databases. If the projects or users are interrelated and should be able to use each other's resources they should be put in the same databases but possibly into separate schemas. More information about managing schemas is in the PostgreSQL 7.3 User's Guide.
Note: SQL calls databases "catalogs", but there is no difference in practice.