From what I know there is a secret sauce beyond a mere AMI and a control plane, based on some EBS volumes magic. I may be mixing things up with Aurora though.
There were some comments in the early days that the Multi-AZ magic for classic RDS was just drbd on top of EBS.
Aurora is a completely different approach where the RDBMS code is modified to directly interface with EBS instead of going through a traditional OS filesystem layer.