MySQL is a relational database management system that has been made open-source by the MySQL development project. Under the GNU General Public License terms and a variety of proprietary agreements, this source code is now openly available.
PostgreSQL works as an object-relational database management system which primarily works to store data securely and return it when requests come throughout from other software applications. In PostgreSQL, the emphasis is on extensibility and standards compliance.
It is highly sophisticated enterprise database system which supports various latest features such as high-availability to cloud services to hot backups of data. It is recommended for development of large data warehouse supporting business intelligence (BI) queries and answer of business questions.
The Microsoft SQL Server is a relational database management system which mainly functions to store and retrieve data at the request of other software applications. These other applications may be running on the same computer or on other computers across networks, which can include the internet.
Oracle Database is a database management system which is object-relational. You may have seen it referred to as "Oracle" or "Oracle RDBMS".
MongoDB is a cross-platform and document-oriented database program which is open-source and available for free. Published under a combination of the Apache License and the GNU Affero General Public License, MongoDB is a NoSQL database program that uses JSON-like documents with schemas.