I usually use “Postgres” when speaking to other developers and PostgreSQL in documents when I can use the capitalised “SQL” for emphasis.
Here’s a bit of history on how the PostgreSQL name came up:
PostgreSQL evolved from the Ingres project at the University of California, Berkeley. In 1982, the leader of the Ingres team, Michael Stonebraker, left Berkeley to make a proprietary version of Ingres. He returned to Berkeley in 1985, and began a post-Ingres project to address the problems with contemporary database systems that had become increasingly clear during the early 1980s. At the time, POSTGRES used an Ingres-influenced POSTQUEL query language interpreter.
In 1994, POSTQUEL query language interpreter was replaced with one for the SQL query language, creating Postgres95.
In 1996, the project was renamed to PostgreSQL to reflect its support for SQL. The online presence at the website PostgreSQL.org began on October 22, 1996.
After a review in 2007, the development team decided to keep the name PostgreSQL and the alias Postgres.– from Wikipedia
Computer History ❤️