In PostgreSQL, the hierarchy is: host > cluster > database > schema > object.

By host, I mean a server. A host can have many database clusters. Usually it has just one. To have more than one, you would have to have more than one PostgreSQL instance running, each listening on a separate port. The default port is 5432. I don't recommend more than one cluster per host. I just mention it as possible.

A cluster can have many databases.

A database can have many schemas.

A schema can have many objects. By object, the most familiar is a table, but there are other kinds of objects: views, functions, custom types, sequences. An object cannot exist directly in the database. It must be part of a schema. The default schema is called "public". Traditionally in other databases, there was a schema for each user. So if jdoe logs in, his default schema is also called jdoe. In fact in other databases this is the only schema a user can have. You cannot make more schemas and name them whatever you wish.

The advantage of a schema over a database is that you can make a query that uses objects in different schemas.

  select *
  from schema1.table1
      join schema2.table2 on table1.col = table2.col

If the tables were in different databases, then you could not combine them as easily. I think you would have to resort to Foreign Data Wrappers.

I have gotten a long way, with many applications over many years, with one host, one cluster, one database, and many schemas.