What is postgresql_psycopg2?
It is (one of) the Python bindings to the PostgreSQL client library. It has nothing to do with PostgreSQL itself other than it allows Python programs to access a PostgreSQL server.
When you connect to your PostgreSQL database, you most likely will use Psycopg (imported into python, allows you to write SQL code and submit it to the database). postgresql_psycopg2 belongs to Psycopg2 (second version of Psycopg), while postgresql belongs to Psycopg (the first version).
As intgr mentioned, if using with Django, Psycopg2 is recommended (Psycopg isn't supported anymore)