PostgreSQL is an object-relational database for applications that need SQL transactions, relational constraints and extensible data types. It also supports JSON documents and an extension ecosystem including geospatial tools. Teams can run it themselves or buy a managed service from a hosting provider; the database licence does not include somebody operating backups and upgrades for them.
PostgreSQL
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MySQL is a relational database used behind websites and business applications. Community Edition provides a downloadable GPL database with transactions, replication and JSON support. Oracle also sells commercial editions and cloud services. A shortlist should identify the actual edition and application support requirement, rather than treating every product carrying the MySQL name as the same purchase.
MongoDB is a document database that stores records as BSON documents and supports queries, aggregation and transactions. Teams can operate Community Server themselves or use MongoDB Atlas hosting. Its data model can suit applications organised around documents, while schema validation, indexes and cross-document requirements still need deliberate design. Atlas Free is a constrained development entry point rather than a promise of unlimited production hosting.