Every PostgreSQL database contains some objects that are brought in automatically when the database is created. Every user will find a pg_database system catalog that lists databases, as shown in the Listing databases on this database server recipe. There is little point in checking whether these objects exist, because even superusers are not allowed to drop them.
On the other hand, PostgreSQL comes with tens of collections of optional objects, called modules, or equivalently extensions. The database administrator can install or uninstall these objects depending on the requirements. They are not automatically included in a newly created database, because they might not be required by every use case. Users will install only the extensions they actually need, and when they need them; an extension can be installed while a database is up and running...