The correct choice is a service that offers a fully managed database compatible with PostgreSQL. Amazon RDS (Relational Database Service) is specifically designed to handle relational databases, including PostgreSQL. It simplifies the setup, operation, management, and scaling of a relational database in the cloud. This means users do not need to worry about the underlying infrastructure, backups, patching, or scaling, as these are managed by Amazon RDS.
AWS Aurora, another service offered by Amazon, also supports PostgreSQL compatibility and is known for being a high-performance relational database. However, it is a specific implementation of RDS. While it provides more advanced features and optimizations, the general statement about compatibility with PostgreSQL most directly aligns with the services offered under Amazon RDS.
AWS DynamoDB is a NoSQL database, which means it is designed for unstructured data and does not support relational database features like SQL or transactions as found in PostgreSQL. AWS ElastiCache is a caching service rather than a database, focused on speed improvements for applications by providing in-memory caching. Thus, those options do not pertain to a fully managed PostgreSQL-compatible database.