In a PAAS system, the DBMS is a separate service. For Amazon, it would be 亚马逊 RDS. Just like with Elastic Beanstalk, where you don't have to worry about the application server and you just upload your WAR file, with RDS, you don't have to worry about the DBMS and you just deploy your database(s).
Finally, using Elastic Beanstalk doesn't cost anything more than the deployed resources (EC2 instances and the load balancer). However, RDS is not cheap and would definitely be more expensive than using a single EC2 instance for both the application server and the DBMS.