Chapter 21. Managing Databases of Postgresql Manual
Server > Database > Schema > (Table, Function, etc.)
Database is top-level in hierarchy of objects. One connection connects to one database. Databases are physically separated and it's recommended to use multiple databases if the projects are unrelated and do not share anything between them.
Database is a collection of schemas, which contain tables and functions, etc. Schemas are logically separated and access is controlled by privileges, etc.
Tablespace enables administrator to define locations in file system for storing data in databases