Aurora is a binary compatible (Mysql, PG) API over an internal AWS infra/storage layer that provides cross-AZ redundancy and transparent scaling. Storage is replicated 6 ways across 3 AZs. You still need to define the "compute" component as an EC2 instance, but storage is not via EBS. Read replicas are compute only, storage is shared. Backups are continuous to S3.

RDS is a managed database "cluster" (in the PG sense of the word) running on EC2 infra. You need to define both compute and storage. Backups are snapshots, not PIT. Replicas are via the standard DB engine replication,