Question

Coming from MySQL and not knowing about ROLEs I absentmindedly tried this

GRANT CREATE ON TABLESPACE pg_default TO username;

It didn’t have the desired effect. The command that I was looking for was:

ALTER ROLE username WITH CREATEDB;

But what’s the difference precisely? Does giving someone the CREATEDB role implicitly give them CREATE ON TABLESPACE …? Is there a table where I can see all this?

From the docs, GRANT CREATE ON TABLESPACE means (my emphasis):

For tablespaces, allows tables,
indexes, and temporary files to be
created within the tablespace, and
allows databases to be
created that have the
tablespace as their default
tablespace. (Note that revoking this
privilege will not alter the placement
of existing objects.)

Answer 1

They are completely different privileges. CREATEDB means the role can create database. If your role doesn’t have that, it can’t create databases, period.

Granting CREATE for a tablespace to a role means that the role will be able to use that tablespace as default tablespace for the database. So a role that has CREATEDB will be able to create a database; just not on that tablespace. Note that there’s always a pg_default tablespace that will be used as default tablespace for databases that don’t otherwise have a default tablespace.