The Structured Query Language (SQL) is a language for managing relational databases. There are many different dialects of SQL based on the unique database engine, but the core of SQL is the same.
Popular Database Management Systems
A Database Management System (DBMS) manages databases using SQL.
SQLite
SQLite is a lightweight DBMS that stores all data in a single file, which is useful for embedded systems for a small database with limited processing power.
MySQL
MySQL is currently the most popular DBMS for scaling production
MariaDB
MariaDB is a drop-in replacement for MySQL due to the ownership of MySQL by Oracle. Here is installation instructions.