RDBMS

(Relational DataBase Management System) Software for storing data using SQL (structured query language). A relational database uses SQL to store data in a series of tables that not only record existing relationships between data items, but which also permit the data to be joined in new relationships. SQL (pronounced 'sequel') is based on a system of algebra developed by E F Codd, an IBM scientist who first defined the relational model in 1970. Relational databases are optimized for storing transactional data, and the majority of modern business software applications therefore use an RDBMS as their data store. The leading RDBMS vendors are Oracle, IBM and Microsoft.

RDBMS usually include an API so that developers can write programs that use them.
Typical RDBMS include
Microsoft Access
Microsoft SQL Server
Sybase (The forerunner of Microsoft SQL Server)
IBM DB2
Oracle
Ingres
MySQL
Postgres