Amazon Aurora is a fully managed MySQL- and PostgreSQL-compatible relational database built for the cloud that combines the performance and availability of traditional enterprise databases with the simplicity and cost-effectiveness of open source databases.
Amazon RDS (Relational Database Service) is a managed SQL database service a relational database in cloud which makes it easy to provision, setup, patching, and backups. It supports Aurora, MySQL, PostgreSQL, MariaDB, Microsoft SQL Server, and Oracle database engines.
RDS is compatible with MySQL, PostgreSQL, MariaDB, Microsoft SQL Server, and Oracle.
Aurora is compatible with PostgreSQL and MySQL.
Aurora offers higher availability and better durability than RDS, due to its unique storage model, and ability to perform continuous backups and restore with a very low RPO (recovery point objective).